This page explains in detail the interactions between the Donkey Kong series and the Hyokkori Hyotan-jima series.
Donkey Konga (Japanese version)
December 12, 2003
Donkey Kong Hyokkori Hyotan-jima
The Japanese version of the game features the Hyokkori Hyotan-jima opening theme as one of the playable tracks.
See here for other songs featured in the game.
License
The creators of Donkey Konga were licensed to use the song by its owners.