A Girl Gamer is a Girl that plays as much videogames as a Gamer
While most people believe Girl Gamer = 'not good looking' as being not that good looking this is more a stereotype than anything else, and more or less a value judgement.
Also note that Girl Gamers are not just videogames, but any type, whether they be board, Pen & Paper RPGs, or Collectible Card Games
Girl Gamer's are a rare species, and those that do exist are hunted to extinction by the Guy Gamers.
Here we see the Girl Gamer in one of her natural habitat, an internet cafe playing a rousing round of Team Fortress 2. We see the male of the species sit next to her starting up TF2, clearly trying to gain her attention.
Male Gamer: "So are you seeing anyone?"