First of all, thanks for the love for Ori on this thread, much appreciated.
To answer the original question, I'll make a few recommendations
Bioshock (Garry Schyman)
No-one can compose like Garry. He has his own language. His work on Bioshock is extraordinary.
Hellblade Senua's Sacrifice (David Garcia & Andy LaPlegua)
This game in particular does an incredible job of marrying dialogue, SFX, ambience and music into a cohesive experience WITH the gameplay/story. It's no surprise that David Garcia is in-house at Ninja Theory. For me it's one of the best audio experiences ever committed to the medium.
Assassins Creed series (Jesper Kyd and many many others)
The series just in general has incredible music.
Remember Me (Olivier Deriviere)
Olivier Deriviere is in a league of his own in matching music with gameplay and implementation. But he is able to combine his integration skills with musicality, which is quite rare.
This score combines live orchestra with glitchscape that ties into the memory fragmentation that is a huge part of the plot and gameplay.
On the jazz side of things, check out LA Noire, and Grim Fandango. Enjoy
Lastly, you don't
*have* to be a gamer to score a game well. But in the cases of those who don't, they are usually working with an outstanding audio director or music team that is going to take the stems of their recordings and implement / breakdown / re-arrange for them, this was the case in Spiderman, God of War, and many other games, especially at the AAA level where so much music is required.
Especailly in the case of games with any kind of narrative, you need to have a basic understanding of what the player is going through. You simply cannot understand that if you are not holding the controller and taking part in the interactivity in some way. It may be conveyed to you in a video, or even by an audio director, but, that brings me to my next point...
...When you're starting out, good luck getting an audio team that is going to be that dedicated to getting your music to play back properly in the game! You are going to need to do it yourself, or at least have some understanding of what you want so you can give it to a programmer so they can set it up for you. Resources are stretched so thin at the indie level that getting any time allocated for programming is quite hard. The better understanding you have of the game and how you want your music played, the better it'll end up being implemented. You can get this done without having any FMod or Wwise knowledge whatsoever, but you still need to be able to communicate to a programmer what you need.
It is true that it is possible to write music for games and treat it like a film score or a concept album. But this is the bare minimum (and sometimes that is enough depending on the game).
But those doing the best work in our medium are either playing the games or have a great audio team supporting them in their work. It's not
music for games, but
game music. There is a subtle but important difference, and to be frank, not that many people get this. The more you understand how music can connect to a player when it comes to the gameplay experience the better your chances of delivering great music for the game you work on. How you do this is up to you! But playing the games themselves is in my opinion, by far, the easiest way to gain this understanding.
Thanks for reading if you got this far!