The video game awards happen once a year, https://thegameawards.com/

Video game genre will be defined by Wikipedia, https://en.m.wikipedia.org/wiki/List_of_video_game_genres

For example, if a shooter is the winner then the action category wins per Wikipedia.

This question will resolve when the 2024 Game of the Year winner is announced. If a game is multiple genres per Wikipedia then multiple options will resolve yes.