The core mechanics of the game are the same: Draft pups, play them, and they will perform tricks that allow groups of pups to bury bones. Bones are worth points, and can be upgraded by various tricks to be worth more points, and end-game bonuses can upgrade them as well.
The new Rascals have Schemes! If you complete a Scheme, that group of pups will double all their points at the end of the game.