In fanfiction, an anonymous girl gamer can be depicted as highly intelligent. She has to understand complex game mechanics, develop strategies, and adapt to different situations quickly. She might also be a bit of a loner at first, more focused on her gaming than socializing, but as the story progresses, she starts to open up to others in the gaming community. Moreover, she could be very creative, coming up with unique ways to play the game that others haven't thought of.
She can be characterized as tenacious. Since she's in a competitive gaming environment, she has to keep trying even when she fails. For example, if she loses a big match, she'll come back stronger.
She can be seen as passionate. Her love for gaming is what drives her. Whether it's spending hours practicing a new move or staying up late to complete a difficult level. She could also be rebellious in a sense. Maybe her family doesn't approve of her gaming so much, but she defies them to pursue her passion. And she might be a bit of an underdog, underestimated by other players because she's a girl, but then she surprises everyone with her skills.