They hate bro gamers, and will generally not look upon casual gamers as well, though they only truly hate casual gaming. Everything else about them fits well into punk, indie, sometimes hipster, and once in a blue moon perhaps emo. But if a scene kid is ever one of these... well that's almost impossible.
Games with grungy, punkish or even just indie soundtracks are a subject of enjoyment especially.
No More Heroes, Scott Pilgrim, Mega Man 9 are modernish punk games.
Final Fantasy II, Mega Man 2, and Dragon Quest are examples of games that are often talked about and referenced.
Punk Gamers do NOT play:
FPS Games (unless they're retro like GoldenEye, Doom, or Quake)
Gimmicky games (especially not these)