'twitch' in games typically means latency-sensitive, like a competitive FPS where being 10ms faster to shoot than the other guy means you win the round. Many games can handle 100ms of latency no problem, so running at 50fps instead of 60fps is no big deal. On consoles those games typically run at 30fps to begin with, which is at minimum 16ms more latency than playing at 60fps on a linux or windows PC.