Subject Toast, nope. It's the Nightmare Before Christmas: Oogie's Revenge. This happens after the Nightmare Before Christmas. Jack leaves Halloween Town to discover new scares for Halloween and while he's gone Lock, Shock, and Barrel bring back Oogie Boogie. Oogie then proceeds to take over Halloween Town and kidnaps all the other leaders of the Holidays and steals their doors that will allow them to go to there world. But before Jack left town he was given a weapon by the doctor that you use in the game. You have 3 forms. Normal Jack with the Soul Robber, Pumpkin King Jack who is the scarecrow and you have fire attacks, and finally Santa Jack with modified presents that can freeze enemies, started them, confuse them, or stun them.
That is just the cutscene of the battle. You actually have quick time events during this.