The gamer equivalent of the Arrogant Kung-Fu Guy. He's a Hard Core gamer, plays in all tournaments, and knows everything about how to play. He knows all the secret moves (even the glitches), the most effective strategies, and the quickest ways to completely destroy his opponent. He's completely "above" the mantra of casual play: He doesn't play just for fun, he plays to win. He's good, and he knows it. There's nothing wrong with that.
However, he's also extremely arrogant. He's completely intolerant of play styles other than his own. If you challenge his beliefs, he'll automatically call you a Noob, a Scrub, or something similar. As far as he's concerned if you don't play like him you have only your inferior skills to blame, because obviously you would if you could.
This kind of player takes the "pro" mentality to an annoying extreme, generally giving other tournament players a bad name (while his counterpart, the Scrub, takes the casual mentality to an annoying extreme and generally gives other casual players a bad name). In the real world, there's room for both, and game companies generally try to put something in their games for both Player Archetypes.
In the end, what makes a "Stop Having Fun" Guy isn't the rule-setting, it's the attitude. While regular competitive/tournament players simply like playing to win, the "Stop Having Fun" Guy believes that this is the only right way to play the game.
The SHFG is a specific subspecies of Fan Haters, who dislike/condescend to "casual" gamers who don't play the same way they do. It also overlaps with Complacent Gaming Syndrome, where the players use only one or two characters/strategies/levels to make winning easier.
See also: Scrub, Serious Business, Fan Dumb, The Killjoy and Internet Backdraft. The larval form of the SHFG is the Munchkin. See It's Easy, So It Sucks! for the mentality that sometimes results from the single-player form of this. When the game itself has this mentality, see Easy-Mode Mockery.