Blockchain is a means of tracking information, typically virtual balances, usually with full history - but it varies in its level of decentralization.
While one of the big uses of blockchain is distributed trustless consensus, that is by far not the only use. It’s also great for inventory tracking - virtual or otherwise. Decentralization is just a kind-of bonus for redundancy, in such a case.
Systems already exist for blockchains - fast ones, too. They can use existing open-source code.
What benefit it provides is that only official Blizzard tokens are on the chain - each one signed (in batches, of course) offline by Blizzard in an official ‘printing’.
Someone discovers an exploit that gives them more tokens? The answer is ‘from where, and who signed them?’
Now, this doesn’t prevent someone who has a hacked system from getting screwed and losing all their items. But it does prevent magic item gain just because you fiddled with the interface in a certain way, and a counter went up.
It also means that, if you did somehow find a way to steal, the history of that is there, and the transactioms can be reversed.