There's two kinds of serious gaming, in my opinion. The first kind is the one with which we are familiar that tends to drive all the fun out of the game: the hyper-competitive, "winning equals life, losing equals death" type of serious where too much weight is placed on the meritocracy of winning (this is an attitude in which no mistake is tolerated). Under this kind of serious gaming, the gamer is focused on being the VIP or superstar of the game that carried the team to victory, and he desires this to be the case every single time. It's entirely focused on achieving bragging rights for having the most points, kills, highest score, or whatever.
The second kind is more about maintaining focused attention on the game, being aware of the situational changes in the game, and adapting to those changes. You still play to win, but you are more focused on the nature of simply playing the game properly and to the best of your ability rather than the meritocracy of winning or losing. Under this kind of serious gaming, you are focused on understanding what the key objectives are, what actions are most important to execute, and learning to set aside distractions (such as chasing kills) that pull you away from the primary objective or targets. It's about being able to read the flow of battle and adapt accordingly. Also, under this kind of serious gaming, you are more focused on actual teamwork rather than trying to be the singular superstar that carries the entire team to success (it's always interesting to watch an American Dream-Team olympic basketball team get drilled by some random foreign team using nothing but basic 101 tactics and teamwork. The reason the American team would lose is because the players are too concerned with show-boating and competing for who does the most work to carry the team). You focus on what your specific task is, and you do it, even if you are stuck at a flag or point doing boring guard-duty to keep some stealth character from ninja'ing it. The fact you stay and guard that point could make the difference between being able to win or lose (I can't tell you how many times I used to see a team lose Arathi Basin in WoW because no one wanted to stay and guard the flag). Under this kind of serious gaming, you let winning and losing take care of itself, and you just focus on playing the game.
As I see it, the basic problem is that winning and losing, for many gamers, has become the metric by which they measure the worth and value of the person. Their own sense of self-worth, self-esteem, and value in themselves as a person is being too much predicated on their ability to achieve a high win/loss ratio, most points, most kills, highest score, etc. This entire attitude of being "pro" is an unreasonable expectation that everyone should be able to play at the same level and skill as the top 5% of players (an obvious contradiction of possibility). So, they stop focusing on the playing and instead focus on just the numbers.
I don't know if any of that makes any sense. I rattled this off stream-of-conscious-like, so it may not be entirely consistent.