Hm... I'm honestly not sure how to answer this. A possibly better question might have been if there was a problem with the concept existing, i.e., if the idea of Gamer/Geek/Nerd girls should be considered separate from the idea of Gamers/Geeks/Nerds. If you put it like that, then yes, there is a problem with the concept existing because there is no reason for G/G/N to be differentiated based on gender. And this, of course, doesn't take into consideration the potential unnecessariness of the existence of the concept of G/G/N of any gender, because I believe people should just be allowed to do their own thing.
On the other hand, if you want me to take the question at face value: is there a problem with the existence of girls who are G/G/N, then the answer is No, because, again, everyone has a right to like what they like as long as it doesn't harm anyone.
I just hate all the ditsy little girls who pretend to be into all that stuff just for guys' attention. It makes the rest of us look bad. Or the ones who scream to the world about how much of a "geek/nerd" they are. It's kind of like, can't you just be into what your into without shouting it in everyone's face in some silly attempt to look cool?
Like, sure, I grew up playing video games and being into things that would be considered "nerdy/geeky". A lot of my interests are adopted from my parents (for example, my mom is super into Starwars, and so I like Starwars too because we watched it when I was younger and I enjoyed it), or are the product of the fact that I grew up around guys because I mostly hung out with my younger brother and his buddies as a kid (and still do a lot). But to me, it's just something that I enjoy doing and that I'm interested in. I don't do what I do to be cool, I do it because I enjoy it. I just can't really stand all these silly little bimbos flapping around just to seem interesting (and guys do it too, y'all are just as guilty of doing things to try and look cool or get attention, seriously).
......... I didn't think there was a problem except for usual sexism. Are that many people really bagged on for being a female geek/nerd? I don't usually see people with a problem about a player being female, and when it was, they were just over-all sexist.
As a geek/nerd/gamer girl YES! there are so many problems for us. If anyone finds out I'm a girl while playing COD I will get at least 5 date proposals in three seconds. Then people start treating me differently, either focusing on me going extra hard to 'prove she can't do it' or going easy 'because she's a girl'. And that's just one thing.