I kind of understand where the anger about "fake" geek girls comes from. It's sort of like the "nerd" costumes they sell for halloween - it's putting on the dressings of a stereotype for amusement or other gain. It's not far removed from blackface.
But the issue really is determining who is a "genuine geek", and that's what people who are angry don't understand - anyone can be a geek if they want to. Some people think they're born geeks and have always been and always will be geeks, and anybody who's only getting interested in geeky stuff later in life doesn't count (particularly if the newcomers didn't suffer when they were young).
What really brought the issue to the fore is "geek chic"; the co-opting of certain clothing and accessories once the sole domain of "true geeks" and nerds into mainstream/hipster fashion. Teen girls made that stuff cool all of a sudden, and people like in the comic who have only ever played angry birds called themselves geeks. Like many teenagers, they just went along with what was cool whether they were actually interested or not.
Of course that's only one aspect of it, another thing is stereotypically "hot" women gaining visibility as hosts on the G4 TV channel, youtube shows made by game magazines, etc. It'd be easy to imagine those places simply hiring models and actors, and I guess that's what people assumed... though it turns out that most, if not all, of those people are like the author of the comic - they are actually into that stuff, but they're also girly or whatever and don't dress like a geek stereotype.
In any case, what it comes down to is what was once social suicide for non-geeks, stuff like gaming and whatever, is becoming mainstream. Like in the comic, nobody in high school now would think twice about anyone of any type if they said they're into videogames.
That said, there's certainly different levels of geekiness. It's like the word "hipster", which is used so generically it's lost meaning. It's becoming harder and harder to label people - a good thing - and soon I think the word "geek" will lose a lot of the meaning and connotations that it has now.
And all the assholes who make nerdy and geeky stuff hard for females to approach can go fuck themselves (not like anyone else will, anyway) - they'll disappear over time too.