Hhmm... so how would the proof of work?
I've been thinking about this and it is quite difficult, but probably not impossible.\
If I am Kasparov, and you beat me at chess, I think that is good proof of work. If you lose, then it doesn't prove anything. So winning chess games should be linked to block creation.
You'd need a way to score players so that you know if someone beat a good player (= proof of work) or a bad or unknown player (= proof of nothing).
You'd need a way to prevent or discourage fake opponents too, that lose on purpose to give score to others.
I am thinking of something along the lines of pools of players.
Pool 1 has 10 players, Pool 2 has 100 players, Pool 3 has 1000 players etc.
And you get promoted or dropped down from pool to pool based on your play, with rewards going to winners in the higher pools.
But the details are not completed in my mind yet.