I’m not saying it’s impossible, of course, just that a lot of really smart people have been working on this problem for almost a decade, without having a production-ready solution yet.
A good discussion of the challenges is at their sharding FAQ: https://github.com/ethereum/wiki/wiki/Sharding-FAQ
Isn't that the approach taken by the Lightning Network for Bitcoin?
I think it's totally fair to say that Lightning technically isn't production ready, but it does seem to be in the late stages of testing / early release candidate stage of development.
This is the same way that the lightning / plasma network works, right?
In the case of a game, this might be simpler since you can have each player sign their own moves and the other player's last move, so that you can always broadcast your opponent's last move if they quit.
http://www.blunderingcode.com/a-lightning-network-in-two-pag...
What makes more sense right now, for many games, is to put most of the state changes off-chain. If players are taking turns, they can sign the state changes as they go, and submit the final couple moves to the blockchain. Add in another trick and you can even make fair random numbers: http://www.blunderingcode.com/gamble-channels-fast-verifiabl...
This is how FunFair works; there's an on-chain transaction to deposit, another to close out and withdraw, and in between you can gamble all day without waiting for blocks or issuing transactions to the blockchain.