This was intended to be a licensed, horizontal-scrolling desert racing game based upon the movie. It didn’t get very far in development before being canned.
A "Buckaroo Banzai and the Hong Kong Cavaliers" arcade machine appears in the movie, but it's believed to be a film prop made from a Star Trek upright cabinet. Unsure if related to the actual machine in development at all.
A rumor exists that a laserdisc-based arcade game was tested at the Boise State University Student Union, but it's just a rumor.