Much smaller differences in latency have been shown to be relevant to competitive FPS (it's not necessarily absolute reaction time but relative to your opponent

Much smaller differences in latency have been shown to be relevant to competitive FPS (it's not necessarily absolute reaction time but relative to your opponents that matters). That said it's unlikely to be entirely the decider for a lot of people. Also, that kind of latency is basically the best case scenario: when you factor in a not-fantastic internet connection, location, and wifi, the user experience could still wind up quite poor in a lot of games (and it's not something which all players are going to notice consciously, they're just going to feel like the game controls worse).