No, the chain only has authority over itself.
It's the same issue as with NFTs. Yes, you can store on the blockchain stuff like "User 0xabcdef owns the Godslayer of Hitpoints sword". And a game can look at the blockchain, and make use of that record.
But absolutely nothing whatsoever stops it from deciding to stop caring, or replacing your fancy sword with a rubber duck, or deciding that screw this particular user, they're banned regardless of what the chain says.
Also even to the extent this stuff works it's not nice to use. If the blockchain has you have some sort of resource (money, quota, etc), then if somebody ever gets their hands on your account they're now the rightful owner as far as the blockchain is concerned. So if per the chain you're owed say, 1 year worth of GPU time or something, that automatically becomes a self-paying bounty. Everyone can see it, and has an incentive to try and hack you.