Recommend me a game > Get on wishlist

I'm not sure if you played, but I recommend Bastion and Transistor. They have their share of action, but are also very emotional, in part thanks to their amazing sountracks that complements the story and the characters.

I also recommend The Swapper. Is kind of a metroidvania, but have no combat, only puzzles. Kinda short, but is very philosophical and makes you wonder about a lot of stuff.

Finally, Event[0] is a great game where you're alone in a space station and you can talk to the main AI (actually typing questions and comments). Very mysterious and have multiple endings, depending on what you do or say to it.

Inside
Never Alone (Kisima Ingitchuna)
Last Day of June

All the recommendations above have a rich narrative, two are platformers and the third one is an adventure.

By far my top recommendation for rich stories are Japanese Visual Novels though.
Phoenix Wright: Ace Attorney Trilogy rocks, with wonderful characters and a great chemistry between them.
And then there is Spike Chunsoft, with their Zero Escape and Danganronpa series. Equally crazy and awesome.

Plague Tale, Sunless Sea, Hyper light drifter

Thronebreaker: the Witcher tales. It doesn't have "combat" because it's a card game. The conflicts are more puzzles. The story slots in perfectly to the Witcher books and games lore and is very much about the journey

If it's about experiencing a nice story, I recommend point & click games, like The Night of the Rabbit or The Whispered World with an imaginative story, or A New Beginning where it's a bit more serious and emotional, or the Deponia series where it's often funny, but especially towards the end it gets very emotional and gripping. There are no fights, you can simply dive into a world with a nice story. You have to think a little bit about how you can overcome some obstacles, but I think it's possible. You can really immerse yourself in the story with point and click games.

Furthermore, the Life is Strange titles are definitely recommendable. Also no fights. In the foreground is the story of the protagonists. Life is Strange 2 was the best for me so far, because you experience an exciting story in form of a long journey taken by two brothers, which can change depending on how you do things in different situations. Therefore, there are also many different endings.

And if you also like to go a bit in the direction of horror, then you have to take a look at Fran Bow. Scary elements and very emotional inside.

What I want to mention at the end is Submerged, where it is about exploring a world that is under water to find a cure for your brother. Also without fights, the exploring is in the foreground.

I'm sorry if this is a bit much text now, but maybe you'll look over it when you find the time :)

https://store.steampowered.com/app/230820/The_Night_of_the_Rabbit/
https://store.steampowered.com/app/268540/The_Whispered_World_Special_Edition/
https://store.steampowered.com/app/105000/A_New_Beginning__Final_Cut/
https://store.steampowered.com/app/214340/Deponia/
https://store.steampowered.com/app/532210/Life_is_Strange_2/
https://store.steampowered.com/app/362680/Fran_Bow/
https://store.steampowered.com/app/301860/Submerged/

Ok, here's my recommendations, I'll do a couple with different qualities:

Grimm's Hollow: Short, free, emotional RPG game. This is based on the Undertale example. It's also an RPG, but the main focus is the journey, and the mystery within the game. Your basically a girl that suddenly gets sent to a sort of purgatory and are assigned as a Grim Reaper.

What Remains of Edith Finch: Heavy narrative focus, and considered a masterpiece among many. You explore the mystery deaths of the Finch family, recalled as you go through the families mansion. Gamplay is heavily varied, but simple.

Wuppo: Combat is there, but the focus is more about exploration and solving problems in the world. World feels lived. you start off in a hotel, you get to meet different tribes, and eventually you travel to a city environment. If you like interacting with NPCs, this ones awesome. Mostly humorous tone.

The Talos Principle: I'm not exactly sure if this one fits, but you won it on steamgifts, it's pretty journey focused, and among my favourite games. The focus is on solving abstract puzzles, and the story is there, but your not forced to engage in it. It talks about existentialism and artificial intelligence. Even though the main focus is the abstract puzzles, the puzzles are located in open environments, so you get a blend of exploration.

This is from a completely different discussion, but you might like some of them here:
Click here

Finally I'd look into point and click games and if your really down to pure story, I'd even look into visual novels (I see some good ones recommended here).

Have you tried Never Alone? It's both beautiful and interesting. I don't remember quite well, but game offers stories in both pictured art and videos. DLC is also really deep.
Another one I can think of os Outland. Don't remember what's that about but I know I liked it.

Heaven's vault
https://store.steampowered.com/app/774201/Heavens_Vault/

You play an archeologist who goes from planet to planet to explore ancient ruins. It's a slow pace and there is no battle in this game, it's entirely about deciphering an ancient imaginary language, to discover the universe lore and what is "heaven's vault" and other mysteries.
(as the game progresses you discover words, and little by little, thanks to the context and logic, you discover the meaning of the sentences)

(cowoth is right, 11-11 memories retold is outstanding !)

Why don't you try Distraint game series. Both games make the character to go on a psychological journey.

I will have to recommend Fez. It's a great exploration-driven game where you play as a character that can rotate the perspective of the world to explore and solve puzzles. It even has its own number and writing system which you can discover along the way, and it has lots of hidden secrets you can find to add to the puzzle. No enemies to fight, no bosses to beat, just pure exploration.

A Story About My Uncle
An emotional story of looking for a family explorer, and going on a platforming puzzle adventure yourself.

FEZ
A cute pixel art game with platforming puzzles based on shifting the perspective.

And as someone else already posted, the Trine games.

Quickly looked through the comments and I don't see Life is Strange. The original game has a story that, to this day, is still one of the best stories I know in games, books and / or movies. To put it in perspective, I played the game for the first time about 5 years ago and I am a month away from being 22 so I've seen plenty of stories before and after.

Story: I desperately wanted to play the game a second time and I only managed to find the courage to do so 2 months ago. At first, it seems like it's about to be a really fun game, but tragedy is around the corner at most times. It's a sad story so do have tissues nearby if you play it.
Art style is also nice. It's not my favorite kind, but it's still really aesthetically pleasing.
Music is...to me, it's the best soundtrack in gaming. Obviously, I didn't play all the games out there, but I played a fair share.

Final thing is, if I remember correctly, the first episode is always free to play on Steam so you can always try that and then buy the remaining 4 episodes only if you like the first.

PS. I don't really care about the whitelist if I am completely honest, I just wanted to recommend a good game.

I enjoyed the story line. Its all about the journey. No combat. Its all about using your grappling hook. I enjoyed it.
A Story About My Uncle

Both Portal Games
and the free Portal Stories: Mel (need portal 2 for that one)

I thought they had good stories. I would not call it intense combat.
The Last Tinker™: City of Colors
A Hat in Time

I second some of the others listed above that I've played as having a good journey.
Two Brothers
The Swapper
The Stanley Parable

I recommend playing - I really liked all the parts

Fallout

Syberia 1 - 3

RiME: An exploration journey that reveals an emotional narrative.
King's Quest: A little less similar to your examples, but a great narrative adventure game with multiple paths to many of the puzzles. I grew up with the original Sierra games, so it definitely evoked a lot of nostalgia for me.

I can suggest those ones:
Unravel
Unravel Two
Sea of Solitude
Fe

UPD1: also check these gems of gaming industry:
Ori and the Blind Forest: Definitive Edition
Ori and the Will of the Wisps

It seems you have a thing for RPGs. If you have a desire for a classic, I can't recommend Chrono Trigger and Final Fantasy VI (released as FF III in the US) highly enough. I can't speak for the Steam ports. I played them on SNES when they came out.

I was in high school when they were released, so please know that I may be looking at them with nostalgia lenses.

FFVI: I was already a fan of the series, but when this was released, it was the first one that seemed an epic tale. It seemed mature. It was hilarious and heart-breaking. It's a 40-60 hour casual playlength. There are 14 playable characters, each customizable and each with their own special ability. There's a lot more I want to say about the game, but if you go in blind I don't want to ruin anything for you.

Chrono Trigger: The game that invented New Game +. You go on a time traveling adventure that begins by accident, and you chase a horrifying entity through time to protect the planet. Things in the past affect the future, for good and bad. This game has 15 or so endings, only a couple of which are available on the first playthrough. After you beat it, you start your new game with your strength from the end of the game. You now have the option to fight the final boss at any point, and doing so at a certain point in the main story will give you a different ending. Some are joke endings, some are happy, some are sad.

And the music on both games is absolutely stellar. I can't get enough of both soundtracks.

Very interesting tread as I have the same taste in games.
My favorite: Valley. Just hopping around in this game makes you happy.
Firewatch (must play)
Lifeless planet (first 20 minutes are quite boring but after that it's great)
State of Mind

Beyond: Two Souls
its comming soon to steam .
Really amazing game ,dont wanna say anything about it ,because i dont wanna spoiler
there is a demo you can try out

So... boring games? Ok... lemme think...

Well, noting gets less gameplay-related than a VN. Root Double is a sci-fi mystery novel about several individuals who are trapped in a nuclear facility that is undergoing a meltdown (or at least, so it seems at the start). Has a lot of focus on the characters, their motivations and so on. There are some "action" moment but since everything is shown to you through text and still images there isn't really any urgency for you, the player (although it does a very good job through those images, sound effects and some panning here and there to make the scene seem alive). It actually has a very intriguing and interesting story when it isn't spending hours on end dumping exposition and backstory. :D

Reus is a God Game where you control 4 giants and shape the surface of a planet, creating resources so the little people on it can create bigger and bigger villages. It's not so much a "journey" per say, but I guess you could look at it as you making those little people's "journey" to prosperity. Or something. (Yeah, I don't play too many games without any combat. ^_^' )

Portal 1 and 2. If you haven't played those already, you really should! (Your profile is private so I can't see if you've played them or not.)

A Hat in Time is a very cute 3D platformer focusing on exploration. It does have combat in it, but apart from the occasional boss fight it is pretty simplistic (and very easy).

Long Live The Queen is a stat-management VN about a young inexperienced princess who suddenly has to bear the weight of having only a year until she is crowned queen and having to manage the country. In a very Crusader Kings-like setting where everyone has an agenda and if she isn't competent enough she can get dethroned and/or assassinated.

World to the West is probably the most "journey" game I can think of. It's a metroidvania telling the story about four characters with varying skills and abilities (eventually) working together to achieve a common goal. Yeah, that goal is kinda "stop the bad guy from accidentally ending the world" but, eeeehh, that's mostly towards the end. Has some pretty simple combat, for the most part it's using each character's skills to explore. (It's a sort-a-sequel to Teslagrad, which I guess also counts. It's a puzzle game which, when I think about it, is quite similar to Brothers - A Tale of Two Sons, but not boring and completely soul-crushing. ^_^' )

I'll also have to recommend this game despite it having a huuuge focus on combat, because it's just that good- CrossCode is a game with very very likeable characters and a very interesting story and setting. As you can probably see by just a quick look at it, it does have pretty intense combat (and also lots of puzzles), but everything is just soooo good that I cannot not recommend it. :P

Oh, yeah, I don't really care about the whole whitelist thing. I'm just here to recommend fun games. ^_^'

Another World

They've been out for a while, so there's a good chance you've played them, but Gone Home and Papers Please both had an emotional impact on me. Gone Home is walking sim about a girl's missing sister. In Papers Please, you work at a border checkpoint in a dystopian country.

It's already been mentioned, but Hellblade: Senua's Sacrifice has fantastic character writing. I couldn't help but feel for Senua and all the pain and guilt she suffers.

GRIS
My Paper Boat
Forgotton Anne

You may try them.