There's a trio of composers credited for the film, so I'm not sure who's responsible for this little pastiche. It's a set piece for a dungeon full of non-piano-playing musicians, and sounds several familiar styles of mid-20th century showbiz composers, from the Bernsteins (Lennie & Elmer) to Spike Jones. The strings at the end do a nice job conjuring up George Gershwin.
Musician Dungeon