Girls would be even more into gaming if parents and society in general would stop assigning artificial gender roles to kids. I'm bringing up a girl myself and I'm amazed and appalled at the amount of gender stereotyping that bombards us - and that a lot of parents accept, perpetuate and pass on to their kids - thus creating social stigma for any girl who doesn't toe the accepted gender-role line.
For example: ever notice the bright and/or pink girls vs. dark and/or blue boys sections in kids clothing stores? Ever ask yourself why girls clothes can't be dark and/or blue - I mean surely dark and blue are not naturally masculine. Ever notice the difficulty of finding girls' shoes that are built for climbing on jungle gyms? I often find myself buying boy's shoes for my daughter just because the girl's shoes are too flimsy. Similarly, most girls' clothes and shoes are too light in colour for active use (so they show the dirt more than boy's clothes do).
My daughter loves dinosaurs, but the reaction of parents and store workers to this is telling: "A girl who likes dinosaurs?" they ask, incredulously, as if somehow dinosaurs should a boy's natural domain, and as if a girl who likes dinosaurs is somehow a freak. Similarly, she plays with Buzz Lightyear, toy cars and with Nerf guns. Why these should be considered 'boys' toys is beyond me - I mean what such toys have to do with penises, and why the vaginally-equipped should not enjoy them, is a mystery to me.
And it's not that I'm bringing her up to be a 'Tomboy' - she also has dolls, tea sets, teddy bears and Barbie. I believe in bringing kids up with toys that are interesting: whether they are seen as stereotypically masculine or feminine is beside the point.
The societal gender prejudice is not some vast conspiracy - it's just how things have been done for centuries, and most people are not bright enough to look at the issue with any objectivity or critical judgement. Girls are just mindlessly shoe-horned into the stereotypes from a very young age, and one of these stereotypes is that they don't play video games. There's no reason behind it - it's just a stupid tradition that few people ever think to question.