The mini-game "Jump, Man" involves the player racing against Donkey Kong by running up ramps and jumping over rolling barrels to reach the goal at the top of the stage. This mini-game is a reference to Donkey Kong and its name references Mario's earlier name, Jumpman. Toadsworth's description of the mini-game hints at these similarities with the last line: "Say, this looks familiar..."
Contributed by MehDeletingLater