When Robbie Williams told an interviewer that he felt like a performing monkey, he didn’t mean it literally. But that’s exactly how “The Greatest Showman” director Michael Gracey interprets the remark in “Better Man,” an off-the-wall musical biopic that surely would have seemed banal — as opposed to downright bananas — had it featured a flesh-and-blood actor in the Robbie Williams role.

Gracey takes audiences through all the expected beats of Williams’ career, from his breakthrough as a member of Take That to his record-breaking solo concert at Knebworth, but does so with a CG chimpanzee standing in for the Britpop bad boy. Against all odds, the gimmick works, distinguishing the project from so many other cookie-cutter pop-star hagiographies. If you want to fawn over this boy-band backup singer turned solo superstar for four hours, check out the “Robbie Williams” doc series on Netflix. But if you want to see...