Great thread topic:
The most important game to me musically is SSX 2012, although there is no way I could have known it when I started playing it, and I would have argued prior to the last decade that it would have been THPS.
I had a big move in my life in 2013, and I really redefined my life as well. During the summer of 2013 I moved to Colorado and I had adopted Two Door Cinema Club into my musical repertoire because I was so happy with where my life was; absolutely the best time of my life. I shifted a lot more towards folk and indie music almost immediately after moving to the mountains from my more alt/rap focused music. The Assassin's Creed trailer debuted shortly after my move as well, and that vibed easily into my nature hippiness as well. By the fall of 2013-2014, I was hyped to go skiing; I had always wanted to, but I was finally somewhere that I could make it happen; I made huge life changes to prepare for the physicality of skiing, and I was making playlists to listen to the music on the way to the mountains. Two Door Cinema Club, The Naked and Famous's Young Blood, Theophilius London's - "I Stand Alone" and Lorde [not from a game], as well as throngs of indie/folk and electronic chill music were all featured on that list that list.
Sometime that fall, I watched two snowsports movies. One of them I believe was called "Into The Mind" which may have featured Lorde's "Biting Down", which made me even more hyped to ski to Lorde; but The Art of Flight. My gosh. Even if you're not into snowsports, it's such an incredible movie with an incredible soundtrack. I watch it every year before the start of ski season to motivate me to do leg blasters until I crumple into a pile of goo on the floor. The Art of Flight featured The Naked and Famous' "Young Blood" and "No Way", and perhaps most importantly, M83's "Intro" & "Outro".
This made me realize that SSX was at least, in part, borrowing from the influence of The Art of Flight, which had come out before that game, or at least big-mountain skiing and the rise of backcountry; and was probably trying to craft something based on how awesome that movie is, and that the entire concept of "Deadly Descents" . It also made me realize that whoever crafted the SSX 2012 soundtrack truly cared about what they were doing.
Of interest: Lorde's older stuff, The Naked And Famous, and other various snowsports film adopted songs and artists are all regularly blasted from speakers at ski resorts even though that music is all about a decade old or better at this point.
Anyhow: The list:
Two Door Cinema Club - "Let's Make it Happen Girl" SSX 2012
The Naked and Famous - "Young Blood" SSX 2012
Theophilius London - "I Stand Alone" - SSX 2012
Pretty Lights - SSX 2012 [honestly I didn't even know Pretty Lights was in SSX until just now; but they're a Boulder group so I'm more familiar with them from here]
Rage Against the Machine "GW" - THPS [very likely the first time I heard it] Most of the THPS games was probably the first time I heard a lot of those songs., and I cherish them for what they added to the game, like Goldfinger's "Superman" but they aren't songs I listen to at all.
Bonus: Assassin's Creed something debut used Half Moon Run - Full Circle in a trailer, which is a band I wouldn't have grown into if it wasn't for that trailer. I don't play AC games.