I think he stole it from Renee, the male dancer featured at the nightclub scene!
Or some could say that was his inspiration - which would be funny because some have a problem with Robin Thicke getting inspiration from Marvin Gaye's sound.
there is nothing close to a "moonwalk" in the dance number, just beautiful twisting and sliding -- sometimes on one shoe -- powered by a dance partner, not the male dancer himself.
Renee and Estella were doing a tornillo or 'corkscrew' dance. Here's a nice write up about them. They were very famous in the 30s and are looked upon as royalty for their pioneering Afro-Cuban dancing. Very cool that their work is preserved on film in Another Thin Man.
http://dansetrack.com/rene-estela-a-look-back-at-rumba-royalty/