The valuable thing about an NFT is not any text (as in: link) you embed in it but the fact that it has been minted by someone to mean something. A publisher minting a game NFT would be saying “this token is a proof of license”, same as companies (once upon a time) handed out slips of paper saying “this token is proof of ownership of a share in our company”.
Moreover why would anyone else have an incentive to pay the significant costs associated with hosting a game ownership was on a blockchain, and therefore could be sold independently without them receiving a cut?
You could charge for it. It’s essentially fancy cloud storage. Also, archive.org.