From the Super Mario Wiki
After the player beats the old Donkey Kong arcade machine in Frantic Factory, Squawks the Parrot will appear and tell Donkey Kong to play the game again to win a special prize. After paying two coins, the player can use the arcade machine again. This time though, instead of rescuing Pauline, the player will humorously have to rescue the Nintendo Coin. The game's difficulty also increases, so the player must be extra careful.