See also: trainspotter
Classic arcade games such as Missile Command and Defender require quick reflexes. Unreal Tournament and Quake are more contempory examples.
Typically with these games, you have little time to think. Some players will be operating purely on instinct. The rapid movements they make is where the name comes from. The player will be twitching as they operate the controls.
Sally: He doesn't do anything but drink Jolt Cola, play that game and sleep. He's a twitcher.
If he were then to turn round, open his legs and force his penis back in the opposite to natural direction (his genitals would now be upside down,balls on top) and repeat in quick succession. His manhood would be twitching and therefore making him a Twitcher.