Did I understand it correctly that the genre and gameplay could be any, it just has to be made using the palette? Sorry if it's a stupid question, I want to clarify just in case

Seems like it. There's the optional theme of Fuse, but as long as the game is using the palette it should be fine. And it seems you can use additional colors on top of the ones provided.

Your game's aesthetic must be themed after the palette but it doesn't need to only use the provided colors.