I think the best format would be a side-scrolling beat 'em up like Double Dragon. Jack and Wang tag teaming their way through back alley Chinatown, enemies starting out as thugs but getting more supernatural as they descend into Lo Pan’s nightmare.
Beat 'em ups also lend themselves to retro stlyed games, and Big Trouble in Little China is already oozing 80’s neon charm that I think they’d go very well together.
Jack Burton is player two, I will fight people on this.