Competitive gaming is something very obscure. Competitive gaming, in simple terms, is playing games against a very large scoreboard. There are tournaments and records for nearly every video game published, and not to mention it's actually very fun.
There is competitive gaming of many sorts. Multiplayer, scoreboard, speed run, the list goes on. On one hand, you could use Battle.net to play multiplayer Diablo or Warcraft. You could try your hand at a Galaga High-score at Twingalaxies.com. You could play Super Smash Brothers Brawl in the Major League Gaming online tournament. You could beat Super Mario Brothers 3 in the fastest time and beat the record on Speeddemosarchive.com The list goes on.
But this is definitely not for the faint hearted. The Pac-Man record is unbeatable: It is a perfect score. You can only hope to tie it after painful training. The Super Mario Brothers record can only possibly be improved by frames, Hundredths of a second. If you don't believe me, take a look at this.
Just a small example of what intensity this can bring. This is not something for the weak. If you think you can do it, good luck. If you can't, well, you can always admire.