No, I do not think a blockchain would help with real world RTS because every game is a fresh start and there is little lasting value to the output of the game.

That said, if someone want to issue a currency based upon winners of a game then you could do that. The problem is, that most RTS games depend upon keeping parts of the other player's state secret. With a blockchain that is not possible unless you trust a 3rd party to manage and reveal the state to you as you gain permission.