Not sure if this qualifies as a “game”, but AI robots have been destroying human records for solving a Rubik’s Cube for a while.

https://youtu.be/nt00QzKuNVY

Surely there have to be many others. E.g. table football: https://www.youtube.com/watch?v=UdKBPbV29ek

I'm surprised no one did this maze thing earlier, seems like an obvious idea with high probability of success. And it doesn't even require much in terms of hardware.

A standard demo for robot dexterity is balancing a vertical pole, which probably doesn't qualify as a 'game'.

There was also this PR stunt by Kuka, a German manufacturer of industrial robots, that challanged famous player Timo Boll in table tennis. This was almost ten years ago, not sure how it ended, to be honest.