Subgame

A subgame is a piece of a game—the piece that remains to be played beginning at any point at which the complete history of the game thus far is common knowledge among the players.

There was a subgame that was very well-recieved ^([sic]) in the previous Paper Mario RPG [Paper Mario: The Thousand-Year Door], where you would play through this side-scrolling stage as a gigantic Bowser.