Gaming + Music

Racing games are perfect for this.

Turn-based strategy games.

CS:GO

Simulation games are good for that. I dunno if you're into football but Football Manager is perfect as it has no sound at all!

There are a lot of games associated with music!
Music driven games: (You can choose your own music from your PC)
Beat Hazard
Beat Hazard Ultra
Audiosurf
Audiosurf 2
Symphony
Melody's Escape

Dance:
Electronic Super Joy
Electronic Super Joy - Groove City

Metal:
Brutal Legend

Edit: added Symphony
Edit2: added melody's escape

Puzzle games like Infinifactory and Talos Principle are great for that.

• Depending of the music, I think that Broforce is great. Short levels that are a Blast, fluid and charming to play and relax.

• Also Ziggurat. Kind of similar in concept to Binding of Isaac, but in Sword and Sorcery FPS Roguelite flavor.

• Sunless Sea could be very good too. Very tense and atmospheric.

gemcraft, defense grid
heroes of might and magic, disciples
HoG that don't use sound cues
invisible inc, shadowrun
panoptes, other TCG

I listen to music while playing games in general. But mostly while doing pvp stuff cause it channels my concentration, but most ppl wont do that.....
so I can suggest to you Civilazation, Total War, Heroes of Might and Magic. There are also plenty of J/Rpgs where you can do that.
Hopefully this is helpful to you

IDK, i like to experience the game how it is, so don't really like playing other music over it but there are games like GTAV, truck sim, Audiosurf & such like which you can use your own music in game :)

I'm thinking Cook Serve Delicious didn't require sound cues, but it's been a long time since I played it. Don't know how it'd be if you used your own music.

Audiosurf

Alchemist's Awakening, the music was so relaxing.