So you are either the wish granter or the wisher maker. You are to tell your story as you play the game.
the rules are simple, there are three wishes to be made and the granter can veto (refuse) two of those wishes.
How you go about introducing this game to the characters is up to you but the recommended template is "there is this legend around here" method.
Genre? no limit. you can go with thriller/horror by corrupting the wish or romantic by making it come true in pleasant and interesting ways, etc.
so if you see yourself as a real writer. Let's see you try and impress me your reader.