If the game is able to connect to your wallet and confirm internally that you own the game’s token, it could unlock the game without having to rely on a server.

Sounds interesting, but isn't there an issue that 10 friends could hold a key to the same wallet and all play all the same games, even simultaneously while purchasing just one copy?

I'm guessing implementing this would require some sort of known-file-type attestation distributed app.

I.e. I prove I have a token + link that token to a hash of my current system(s)

It's actually one of the better uses for blockchain I've heard so far, given the data sizes are minimal...

Who is going to maintain this distributed app, and what incentive do they have not to change the code so every game is reported as owned by everyone?

Then can you just duplicate the wallet and you've "pirated" the game

Ah but we'll put it on the blockchain!

...Which is quite literally re-inventing a worse version of systems like Steam

Sure I guess, if you want to share private keys with friends.

Why not just make a separate wallet per-game? You've then effectively duplicated serial keys :)

Who's running the server that actually runs the game?

The idea would work for single player games, where all the content is in the executable, but yeah, multiplayer is another story.

It won't necessarily work for single-player games, since it's trivial to build a game so that it requires a connection to an external server (put in some API with game logic there. Make sure logic isn't easily reversed engineered). Of course, a game company could always make a game which was built to run locally. It's all the company's choice regardless of NFTs, which are as useless as always.