I know what you seek and I've done same research before, the truth is I failed to find one, those projects use normal staking strategy instead of the PoW algorithm, also even if they do I wonder how it's going to work because miners will mine and dump for quick money.
In a world where play 2 earn games are still struggling to have a home this is the last time any developers should come up with.
In the early days of the internet, a lot of companies tried to create their own custom closed versions. They all failed. I think tokens have their place, but I feel that games just staking a bunch of tokens are actually doing the same thing as those people that wanted to replace the internet with their own local version. It is like they are using tokens (or NFTs) as a gimmick and afraid to use a real cryptocurrency.
P2E games have a multi-billion dollar niche already using a token model, so they are definitely here to stay. And to be honest, most of those games would be considered trash if you ignored their NFTs and tokens. There are a lot of ways to drastically improve P2E.
Using a fairly mined POW coin should also encourage people to trust the game economy more. The cryptocurrency is a separate from the game so incidents like what happened to Axie Infinity and their SLP coin couldn't happen.