Originally refers to female fans, though often used for any enthusiastic fan regardless of gender. He's a fangirl of that indie game, just won't stop talking about it.
Pro Tip 2/3
Not Always Obsessive
Sometimes 'fangirl' just means a regular fan without implying obsession. I'm a bit of a fangirl when it comes to classical jazz music.
Pro Tip 3/3
Commonly Informal
Use 'fangirl' in casual conversations. It's not typically used in formal contexts. At the convention, I totally became a fangirl meeting my favorite author.