"Average human response time"
Human response times don't vary very much around the mean. Pro athletes have an advantage in that they are better at anticipating what is going to happen next.
For example a batsman in cricket will read cues from the bowler's body language to determine what the delivery is likely to be. This has been shown in testing of elite cricketers with shutter goggles that blind them at the moment of the ball's release; they are largely still able to defend the delivery based on the information they've acquired up until that point. Among the best bowlers are those able to mask these cues, confusing the batsman.
Anyway the idea that pro gamers and athletes enjoy one quarter of the reaction time of an average human is pretty much nonsense.