The term gamer girl is used by some to distinguish female gamers from the traditional male gamer demographic, but not without controversy. Many girls and women who play video games would prefer to leave their gender out of it. They just want to be called gamers, and see any other label as diminishing their gaming abilities or membership in the gaming community. Other female gamers embrace the term and self-identify as gamer girls.
A different use of gamer girl is sexualized and disrespected. Often called “fake gamer girls” or “gamer gurls,” these women are accused of feigning interest in video games to attract male gamers.
Most people use the terms gamer girl and girl gamer interchangeably. For people who associate the term gamer girl with the negative “fake” stereotype, the alternative girl gamer is a way to emphasize the gamer part of their identity. Girl gamers are a kind of gamer, but gamers first and foremost. On the other hand, the word order girl gamer is criticized for introducing gender where it should be irrelevant. Just as the label “woman lawyer” detracts from a qualification-based recognition of a lawyer who is female, so does girl gamer.
Use these terms with caution. Either one may be considered disparaging when used to label a gamer other than yourself. Referring to female gamers simply as gamers is the safest choice.