The most plausible reason is that computer gaming is generally perceived as a solitary, obsessive, male geek affair. And women, more so than men, tend to prefer communicating about things that don't involve computer games.
But the reason women don't play computer games is certainly not because they're less competitive by nature. Introduce your mother, sister, wife, fiancee or girlfriend to a game such as Lotus 2. Let them practice until they achieve proficiency and then challenge them to a race. Watch several cultural inference sociological power complex theories dissolve as you find yourself crumbling underneath the weight of their new-found skills.
And don't accept any excuses for defeat. Computer games are a neutral medium that don't rely on any particular attribute peculiar to men. If you beat them, it's because they're crap. So rub it in.