"...the exact form the game state takes is irrelevant so long as all players agree on the validity of new game inputs"

From what I understood, trying to generate a canonical state doesn't make sense because all participants had already agreed with the state of the transaction in the first place when it was included in the ledger.

I would say that it makes sense if you have the ability to make the participants agree in the transaction very fast, which I assume is the case of EOS, because you basically have very few of them.
If not, making all participants agree with every transaction would take  longer, that's why I assume you have to pack those transaction in a block and validate it with hashes.