(Which I don't know about, one of the properties God is usually described to have is a willingness to punish defectors.)

If God values punishing defectors enough, then that changes the effective payoffs in the game.

If God's predictive abilities matter, then I take it you're envisaging God in the role of proposer rather than responder, and the sense in which he loses is that e.g. the responder can commit to declining any offer less than (say) $9 from an initial stake of $10, so that God only gets $1. Well. The responder can do that against anyone, perfect predictor or not, and God actually does better than anyone else because he can at least offer the $9 he needs to. But I suppose the point is that the responder wouldn't make that commitment if not playing against God, because without God's magical foreknowledge the predictor won't be offering $9 anyway.

So, anyway, if I understand your parenthesis right, you're saying that it won't play out that way because for the responder to decline a reasonable offer is a variety of defection, and God will want to punish it by refusing to make the offer the responder wants. Perhaps so, but what that means is that God's true payoff isn't (say) $1 but $1 plus the fact of the responder's successful defection, and if he disvalues the second component of that enough it could be worse than $0. Which is true, but it means that they're no longer playing the Ultimatum Game, they're playing another game with different payoffs, and of course that can lead to different choices.