That response time is a different thing. What you are talking about is the response time from seeing something and then responding physically. What this is talking about is the response time from performing an action and the display/sound reacting to it. Those two things are essentially serialized.
When playing online FPS games, anything more than about 50 ms round-trip network lag is starting to get annoying. 200 ms will be unplayable. This was true in the old days at least, but I think many games these days can mask the latency relatively well. They do this by performing the actions locally rather than waiting for the round-trip from the server before performing the action.