"Emotional" Piano Music?

Sorry these're more on the 'pop'-ish side of things, not classical ¯\(ツ)/¯

Nine Inch Nails' super exclusive Still Album (personal fav's 'Adrift and at Peace' , this album's closest to the 'acoustic' experience but it's got some rock parts here and there)
NIN - Right Where It Belongs, Another Version of the Truth (yeah it's noisy at the start but after 1:54 it focuses more on the piano).

Depeche Mode - Somebody,
closest thing to what you're probably looking for: Sibeling

More rock-ish:
Muse - Space Dementia

Electric Wizard - Night of the Shape (does 'spooky' count as emotional?)

OP from Angel Beats - My Soul, Your Beats!
Vocal
https://www.youtube.com/watch?v=zIFV8UUs1-c

Off Vocal
https://www.youtube.com/watch?v=VrG9O7EN8kM

OST from Clannad:
https://www.youtube.com/watch?v=vdk_76z38bA

Funny, I was listening to some stuff that would fit the bill just earlier today. Have some Rachmaninoff.

Dustin O'Halloran's Opus 36

https://www.youtube.com/watch?v=MYVELqMRZRc

love this song.. but strangely, only the piano version can bring me to tears

Random Forest - The Best Of Us

Well, it might not be pure-piano music,; but it is something that I personally enjoy. Some call the style synth-pop.

The band is Leiahdorus (lee-ah-dor-us) and they use pianos quite frequently in their music. I saw Jason and his crew perform live quite a few times and I thoroughly enjoy their music and the emotion evoked by the music. Wake by Leiahdorus

just find the play button on the page
http://s6.picofile.com/file/8265611192/5_2_.mp3.html
http://s6.picofile.com/file/8265611318/14.mp3.html
http://s7.picofile.com/file/8265611400/42.mp3.html

Heh, I actually wanted to suggest most of the stuff from Theishter. But it seems you know him already. I assume you know Aminenz then as well. Other then that I would say the "The Last Door" soundtrack (season 1 and 2) has some beautiful piano tracks although it is not pure piano. Also is more sad/mysterious/moody.

Other than that. Maybe this one(?): https://www.youtube.com/watch?v=i6Zt78NcvaQ or this one (?) https://www.youtube.com/watch?v=JNgeUGcze18

I'll go the opposite way and recommend classic pieces.
Chopin Ballade No.1 is very emotional (so are the other ones 2~4, but I like 1 the best).
For a more simple (but difficult) and beautiful emotional piece, one of Liszt's Etudes, "Un Sospiro" is good. I liked the version played by Hamelin. https://www.youtube.com/watch?v=zSHwX2O7j2w
Also Liszt Piano Concerto No. 2 is good. People usually like Rachmaninoff, but I haven't listened to him a lot yet, so I can't really say.

BWV 846

Gwyn, Lord of Cinder - Dark Souls Soundtrack
lots of Final Fantasy 7 - 9 Piano Covers
lots'a tracks by Ludovico Einaudi

For me, it's Beethoven's Moonlight Sonata (Mvt. 1).
You'll mostly likely recognize it.

parasyte piano

I don't know if the song itself is emotional or if it's just because I read the story about how the guy that made it lost his hearing.

Torley Wong - Xristospiano

archive.org link where you can read the story or download his music if you want.

https://soundcloud.com/julienmarchal
Talented pianist & composer :)

Anything by Suzanne Ciani especially Velocity of Love

https://www.youtube.com/watch?v=zAhZpgeF0qs

Imo most piano "emotional" songs are WAAAAY too cheesy in most cases... I would actually say the first one you've posted its a good example of that XD... the second is alright tho.

I prefer melancholy to be expressed in a more elegant form:

Philip Glass - Glassworks - Closing
Erik Satie - Gnossienne No.1
Michael Nyman - The Piano
Ryuichi Sakamoto- 'Merry Christmas Mr Lawrence'

Now some overly cheesy for my standards but too good to be missed in this topic:

The Cinematic Orchestra - To Build A Home
Ludovico Einaudi - Divenire

This one proved very effective at my father's burial.

Wolf's Rain - Friends

I have an album of minimal piano music myself:

andreimachado.bandcamp.com

I suggest as well Nils Frahm, Ólafur Arnalds, Peter Broderick (that has some folk albuns as well), Max Ricther, Dustin O'Halloran, and so on.

Don't think you'll like any of these, but they're worth a try anyway. Especially the Nine Inch Nails song is my go-to if I want to wallow in melancholy.

Teengirl Fantasy - End
Kneebody & Daedelus - Not Love
Kneebody & Daedelus - Home
Krampfhaft - A Tiny Death In The Family
Nine Inch Nails - Something I Can Never Have

Way back I used to do music myself and tried to compose a few piano pieces. Looking back I could've done them way better, but hey, why not share it for the narcissism. Lose everything. (Let me remove the personal info from the bio first. :D)

2hu piano?