Putting these thoughts on "paper"
Steem transactions don't need to inclue any actual steem or sbd. You can also "transfer" information, or rather, publish it. That's extremely easy to implement on a website using steem keychain. Javascript code on a browser will also allow reading of this data.
You can show some input "buttons" which will broadcast player input and display a game window which is altered by players' broadcasts through steem keychain on the fly, parsing only relevant data to each player.
As long as it doesn't have an intensive realtime multiplayer gameplay, you can pretty much use the blockchain as a server without much effort. Checkers and chess are good for starters, but things like MMOs are not farfetched.
The funny thing is how cheap it is to "host" because the "server" doesn't even need to exist. The game would only read information, not publish them. It would use the player's computer power. Developers might not even need Steem Power since players use their own RC.
Because of how fast the STEEM blockchain is processed alongisde publishing information carries no fees, this might be the ideal enviroment for online multiplayer crypto games.