Right, a blockchain doesn't require mining, that's just how many cryptocurrencies happen to encourage transaction processing. But not all of them do it that way. Ethereum, for example, moved to proof of stake for its blockchain (i.e. you put up X coins and you're trusted as a verifier), so it doesn't need to do any mining at all.
A blockchain is just a series of cryptographically verified transactions. How people are trusted and rewarded for verifying transactions is up to the blockchain implementor.
That said, it's kind of a buzzword right now, so I assume most, if not all, games that include blockchain either do it as a gimmick or do it in a very predatory/scammy way. But that doesn't mean the tech is bad (i.e. email isn't bad because fraudsters use it), it just means it's very niche in usefulness.