I remember reading Grayson Perry's book about men (I forget the title) and he said that was one of the defining features of being a man, that you will find an area to be competitive in. Even men who think they're not competitive because they aren't with things like sports or board games will have something they are competitive about. Take something as mundane as hipster culture. On the surface, it seems like a rejection of the mainstream, but in reality, it then becomes a competition about who knows the most about various obscure references. Even on forums like this (but particularly hobbyist pages, like photography and so on) there will always be one bloke (and it is always a bloke) who has tens of thousands of posts and revels in their status as a respected member of their little corner of the internet. Hell, half of religious bigotry comes from people competing to be the most devout. Things like Twitter supercharge this, where people get followers for being a 'virtuous' person, and actively look for things to be offended by in order to show what a sensitive and enlightened little flower they are. It's certainly not just a male thing, but I think men are more likely to engage in it.
Hell, even on this thread, we risk having a competition to compare who is the most 'above' this sort of material competitiveness thing.