Yeah, this is kind of the thing. I have a social circle with male and female gamers in it, and there are a couple women that are the 'that guy' "gurrrl gamer" type. They play up how hardcore they are and point out their gender soon after, but didn't really grow up with games or learn much about them. Regardless of their motivations, it's a bit insincere, and the other women in our circles distance themselves from them as a result. It's not that identifying as a girl gamer is theoretically bad (being a girl and a gamer at the same time should be as acceptable as being a guy and a gamer at the same time). It's not that a push back against "gaming is only for guys" is bad. It's that the only people that identify as girl gamers tend to be making a point about themselves being special more than they're pushing back against bigotry. People see/think this is happening which then amplifies the effect. Note that several celebrities and activists like Brenda Romero do not identify themselves as girl gamers despite the fact that they identify as women in gaming-- "girl gamer" just has so many negative connotations and seems to attract the wrong people.
The thing is though the type of people it attracts is those people's hangup, not the 'girl gamer' in question's. It's like Erin S Kittens said above, they have every right to identify themselves as a 'girl gamer' or just a 'gamer' or whatever other tag/label/handle they like. Sure they may be 'playing up' the 'girl' part of 'girl gamer', but that's their decision to make.
I can see why some women who play games but don't identify themselves as 'girl gamers' might distance themselves from it, but at the same time they might be selling themselves short occassionally. That girl/woman may be doing it as a means to an end, or they may just be doing it because that's what pop culture has exposed them to. I mean how many times do you see people, both men and women, trying to live up to some fantasy ideal set by magazine covers, underwear photos, and hollywood movies.
Lots of guys wish they had a six pack and cut biceps, and lots of girls wish they had a perfect 34/24/36 frame. Not all mind you, maybe not even most, but lots do wish they looked better, or were better at certain activities, etc. Many folks chase after that ideal in other areas. Gaming isn't much different. Many of these 'girl gamers' might just be chasing after what they think is the 'ideal' image of what being a girl and a gamer is. Maybe its insecurity, maybe it's just because they're trying to make a profitable youtube channel, or maybe heck they just want to be both a 'hot girl' and a 'gamer' at the same time, so they chase after that stereotypical image. I don't see that as a reason to shun them per se.
Some of my best guy friends are gym rats who are chasing after the 'perfect male physique' image. But that doesn't encompass the entirity of who they are as individuals. They're pretty cool guys outside of that, and we agree to disagree on matters of what supplements are toeing the line between good dietary choices and detrimental hormone/chemical additives. Personally I like to go to the gym and work out and stay in shape, but I refuse to spend 4 hours a day chasing that ideal physique just because popular media says it's what I should look like. As long as I'm in shape and can still pass my old military standards of health I'm good with it, but I don't condemn those guys for their choice to chase that image.
Live and let live man. If they wanna be 'gurl gamers' that's cool, or they can be 'women that play games'. The two don't necessarily have to be mutually exclusive either, but in cases where they are just chill out, accept it, and let them do their thing.