Neko to Osananajimi to Mikkakan

I'm an average high schooler. I have a valued childhood friend. Her name is Miyoko. We never dated or anything like that but, we're always together, and that's more than enough. One day, Miyoko brought home a strange charm. That night, she showed up in my bedroom with cat ears. "I have taken this body," said the goddess who now resided in Miyoko. "If you want it back you'll have to win my game!" My eyes were spinning. What sort of game?