I don’t think “domination” is really the correct characterization. Men compete for status, sometimes physically, women compete in different ways. So a guy may hit a rival whereas a women may spread gossip about her.
Gaming is a substitute for some of that physical competition, but I’d also note that physical prowess and competitiveness are perhaps relatively less valued than it was decades ago: in some parts of the country sports like football are disapproved of by many parents (or pigeonholed as lower class). Certainly protecting kids from physical altercations is seen as much more important than in past generations. Part of the point of those physical displays was to appeal to the opposite sex. “Typical boy behavior” as @Rivet2000 says.
If you provide much improved experiences in a virtual world and much diminished experiences in the real world, you should hardly be surprised if the time spent in each changes. And boys don’t spend much time in a virtual gaming world displaying their abilities to the opposite sex or learning how to interact with them.
Girls are spending more time in virtual worlds too, it is just that in general their preferences for those experiences are social networking oriented. As such they may be more depressed than in past years (due to feeling their own social lives are inferior) but those experiences don’t harm their abilities in social interactions quite as much.