It's one half of it; Lightning also needs a "time lock" mechanism to somehow execute payment for the committed balance of the channel if one party unilaterally abandons it. This is quite complex involving both parties holding a delayed and revokable payment from the other party.

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.