Blockchain could be proof of work (i.e. Bitcoin), proof of stake (Ethereum), or perhaps something different entirely. You could even use proof of an account with a central authority if you want.

Blockchain doesn’t really care what the “proof” is, only that it is agreed upon by the rest in the chain.

So if you tie the proof to something like ownership of a key to the game (i.e. a potentially valid use of NFTs, which is rare), then the Blockchain would merely state that 50+% of the owners of a copy of the game agree that the transaction is legit. You could potentially tie it to membership in a server instance instead, so if the main servers go down, you just fork the Blockchain to your instance and you’re off to the races. And so on.

There are a ton of ways to make it useful, but I highly doubt big game companies will go through the effort when they can just stuff a cheap crypto fork in the game and claim they have Blockchain. But that doesn’t mean the tech is useless, it’s just unlikely to be used properly in a gaming context, at least with the current state of the gaming industry.