The blockchain would store users' character data i.e. level, currency, inventory, etc.
It would use a hypothetical form of proof of work where either the previous hash or the nonce would determine what monster and items are available on that server for some given amount of time. Clients would then be required to sign with their private keys a "chain of events" that would have to line up with the server's chain of events somehow.
I wouldn't know how to determine if a client and a server are cheating or not though.
The game developer would imaginably host some of the larger servers and could then sell the cryptocurrency they gain from hosting said servers for some actual fiat as a means to make money.
Clearly this is an incredibly rough idea that I have not actually spent too much time thinking about.
EDIT
an inspiration for this idea was "The World", a fictional game from the dotHack series