The government would probably have your actual identity, while the NFT is pseudonymous. Granted, the government could also do that. Another argument would be that the government probably doesn't want to do it.

Again, if they can be bothered to host the game, I don’t see how a database that’s smaller than most modern AAA games is more likely to disappear.

Who is the actual authority on the database? Are publishers going to trust the stores? The stores the publisher? If the operator goes bankrupt, who is responsible for saving the database and keeping it available? Publishers can't even be bothered to keep selling their own games after a while. It's a liability, not an asset, noone actually wants it.

The blockchain doesn’t need incentives to be slow and unwieldy when it takes hours to confirm a transaction, and a gas war can randomly delay things even more.

You'd be running the thing in a way where that's not an issue. It doesn't even need tie-in with crypto currencies, in the extreme case you need neither proof of work nor proof of stake: All that's needed is a non-fungible token on a public ledger, run by stores and trading platforms: By the stores because they legally need to provide the possibility to trade the license off-store, by trading platforms because that's their business. They would then sign off on ownership transfer to a different pseudonymous crypto key (your identity) upon receiving funds in another way.