I think what's happening, with "fake gamer girls" thing, is that two stereotypes and a definition problem are being smashed together as only the internet can, and the resulting turbulence is what is fueling this "debate."
The first stereotype is that all gamers are smart. And while this may be true in many cases, there are still plenty of nerds that can recite every known race in the Star Wars universe, but can't master college-level math.
The second stereotype is that beauty and brains don't go together; this goes for both genders. No matter where you look, it's very rare to see a smart person portrayed as beautiful or a beautiful person portrayed as smart.
When you put these two stereotypes together, you end up with this logically sound, but still false, conclusion. "All gamers are smart. No beautiful people are smart. Therefore, no beautiful people are gamers."
These two stereotypes are heavily reinforced by modern media, and so, people tend to assume they are true in real life, leading to the distrust of beautiful people trying to "infiltrate" a smart-people club. Since "logically," they can't be smart, and therefore can't be gamers, they must have some other, ulterior motive for wanting to hang around gamers.
These stereotypes play a big role in this "debate." However, I think the biggest problem is that the meaning of the word "gamer" has changed significantly over the last few years.
There was a time when "gamer" meant "one who plays video games." This was because being someone who played video games was the exception, rather than the rule.
Now, with the popularity explosion of smart phones, tablets, and other mobile devices, virtually everyone plays video games, and thus, playing video games is the rule, rather than the exception.
While I can't speak for other languages, I know that in English, we name something that is the exception, rather than the rule. For example, there is no word for "one who is alive and needs to breathe," because needing to breathe is the rule, rather than the exception. Likewise, there is no word for "one who is not a Mormon." The word "non-Mormon" is simply derived from "Mormon," since being Mormon is the exception, rather than the rule.
And so, I believe that the big debate here is actually over what the word "gamer" means. There is a growing number of people who use the term "gamer" in the same way we use the terms "bookworm" or "film buff," as someone who is a connoisseur of games.
According to this definition, someone who only plays WoW or Call of Duty or Angry Birds is not a gamer, in the same way that someone who only reads Harry Potter or the Lord of the Rings is not a bookworm. This does not make them lesser fans of their favorite franchises, but they are not connoisseurs of their respective mediums.
It is this disconnect of definitions that I think is fueling this debate, and the associated nerd-rage that accompanies it. According to the original definition of "gamer," these "fake gamer girls" would be gamers, but under the newer definition, they would not.
Modern gamers are a clique with various customs, social cues, and terminologies, and as such, when they see someone claiming to be a gamer, but matching few or none of their clique's criteria, they are instantly skeptical.
I think it is perfectly valid to see someone (of either gender) enter a social group, with little knowledge of said social group and with no desire to learn about the culture of said social group, and then conclude that the individual has become a part of said social group for some reason other than a love for the social group.
Let me finish of with some clarification. A beautiful woman or man, who shares interests with a gamer and is genuinely interested, is every gamer's dream come true. But, since many gamers have fallen prey the two stereotypes above, or at least believe them, they are extremely cautious with regards to beautiful people claiming to be gamers. Many gamers were marginalized for their interests during their formative years, and thus, they are weary to trust people who, at one time, would have bullied them.
