It would be cool indeed to create monetized chess engine competitions that are public for all to see live. AlphaZero definitely is the top dog right now, but AFAIK only Google has access to it. Could actually base a whole PoW algo off it, as it would mostly come down to the best hardware running the latest engines that take advantage of threading.
The Starcraft 2 Alpha (AlphaStar) was trained on the Google tensor machines for what would in real time be hundreds of years of gameplay per agent, but in the competition it ran on an regular high end cpu/gpu. That was what impressed me the most about it, and I hope that there is a possibility for regular people to get a version of the A.I that they can run locally or over the net.
Training A.I is what takes the computational power, and it looks like ASICs in the form of special purpose machinery is a must to be able to crunch the numbers.