While I usually agree with Jim, and have never complained about the fake nerd girl thing anywhere, I think the video glossed over some important ways in which fake gamer girls are damaging:
1) They damage REAL gamer girls in three ways. Firstly, and most obviously, they add competition in a market for attention unfairly. Given that only a small amount of time can be spent getting to know a person, there is no way for a legitimate gamer girl to 'prove' herself in any useful way.
2) They raise expectations. If it it appears at first glance that gamer girls are common, happy to dress in a slutty pikachu outfit, and usually conforming to ridiculous societal norms of attractiveness, this just encourages unrealistic expectations.
3) If a significant number of women at such events are 'fake' gamer girls, and by nature of being out for attention are more sociable, then they will naturally interact with more people. When this leads to the fairly obvious realisation that they have only superficial knowledge of gaming, then this only reinforces the stereotype that girls aren't gamers.
Also, there was a bit of a (surprising) stereotyping going on underneath Jim's analysis. The assumption seems to be that the majority of male gamers are hideous social outcasts with no hope of interacting with or, Heaven forbid, actually attracting a woman. Should a man actually want to meet up with a gamer girl on the grounds that they are actually interested in meeting someone with similar interests, and not just someone willing to dress like pikachu, then fake gamer girls make this all the more difficult.
So, overall, fake gamer girls can be pretty damaging both to real gamer girls and to anyone who'd like to get to know gamer girls (even for completely platonic reasons) but doesn't have time (or confidence) to speak to everyone they meet and work out if they actually share any interests. This isn't exclusively limited to gaming, it applies to any sub-culture that becomes 'cool'.