Short answer: no, only the final state has to be sent to the on-chain multisig (or in our terminology, the “state deposit”). But this final state doesn’t need to include information about the states that preceded it.

For instance, if we were playing a chess game in a state channel where we each put in 2 ETH and the winner receives 4 ETH, then when the game is over all that happens on-chain (if there is no dispute) is that the multisig receives a transaction that says “Josh:0, Alex:4”, which is then paid out. Someone “watching” the multisig can’t tell that it was a chess state channel, or even that it was a state-channel at all.

If there *is* a dispute, then the participants do have to “show” the multisig that there was a chess game, though again all that needs to be shown is the final move, not the total history of the game.