There is a difference between being competitive and being a jerk. Please try not to confuse the two again.
I've been gaming for ages, I've run servers for dozens of different games, and that line evaporated years ago. Competitive players are 1,000% more likely to trash anyone who 'holds them back', degrading the game quality overall. In an FPS game, the competitive player is going to be the guy spawncamping and abusing exploits, even after he's warned several times that they're against the server rules. When said player gets the permanent boot, I can bet you there's a 90% chance he's either going to get a 'smurf' account and come back to either completely ruin the game with cheats, or he's going to get his clan buddies to come crash the game as well.
Either way, expect to find him on your forums or IRC right after complaining about how you banned him for being 'too good' and that the server is full of 'scrubs' anyway.
Anything taken to extremes can be bad. Competitiveness is no exception. It is possible to be competitive without insulting everyone you play with. There is a difference between being competitive and being over-competitive.
Everyone is competitive, because the point of the game is to WIN. Every game is like this too. The issue comes down to the level of competition you force upon everyone else, and I've found that there's two easy groups. The difference is that to a competitive player, their social skills are so impaired that a meaningless victory should come before everything and anything else.
Another favorite tactic of the competitive player is to join a pub server with a bunch of his retardo teammates and stack one team, landsliding victories in their favor over and over. Again - this ruins games, and when I go in there and break them up, they get pissy and whine.
"Play to win" players, the competitive players, are the tag-wearing assholes who will troll pub servers with aimbots and whatnot just looking to ruin 'scrub' games. Another MO of the 'competitive player' is that they love to troll around on the game forums and try to change the game in a way that benefits them.
Several mods make the mistake of having a 'playtesting team' of highly competitive players. This is probably the worst idea you could ever have. It'd be like giving Stalin his choice of whatever parts of Europe he wanted after WW2. Competitive players obviously care only to win, and advance themselves above anyone else. So you basically end up with exploits and imbalances going unreported, because they know of them and can use them to win. These same douchbags the continue to troll the forum telling everyone who posts to GTFO because 'they're just a scrub' and 'you should watch a clan game noob' and 'I've been playing for longer than you, so shut the fuck up'.
Natural-Selection was a mod that fell into this years and years ago - the game quality suffered dramatically, and the elitist competitive 'scene' basically chased away any new players.
A good tip for the leisure/casual players is to look for clan tag before the persons name. That is a good sign the person is a competitive player. The thinking also applies for the competitive player.
Not very true. Despite the popularity of tags, a lot of tag-wearing douchebags just made it up to wear with their friends, and aren't really playing competitively, or are even actually any good at the game. A good example is Tactical Gamer. All of us wear |TG| tags, but we don't play competitively in any way. We play for fun.
When I run servers though, I profile. People with 'typical' names, like "PeskyFly" would be mostly ignored. Someone with a name that looks dumb and immature like "1Spartan" (sorry, but it's true

Shorthand like 'sk8', etc. generally coincide with idiocy) would be on a 'watch list' mostly because they're usually new. Someone with a clan tag would instantly be Priority 1, as they're most likely to break the rules.
That said, I've yet to see any game truly benefit from competition. A case could be made for, and only for, increasing the longevity of a game, but a game that hovers around in a state of undeath for a few years with a small dedicated group of antisocial idiots vs. a game that simply died years ago, there's really no difference. No new players will be joining the game on life-support, as the high-competition would chase them away.
There was (is?) a game called Allegiance. An interesting project, blending RTS and FPS in an extremely excellent way. The game had the potential to be amazing. It's been 'dead' for a while, with a somewhat large group of competitive players 'keeping it alive'. I joined to play it, and every game was the same way. One team would 'tech rush' to a Frigate or something and roll into your system 5 minutes later and blow up all your stuff. Whoever got this ship first won. Every time. Nothing changed, because it was the fastest, easiest way to put another notch in your belt. The competitive players keeping it alive would say 'we'll teach you how' and the like, but never changed in their execution of stagnant, boring, crappy games over and over, just to win. And if you lost? Prepare to be blamed for it.
Again: I've yet to see any game truly benefit from competition.