is the decision to give up $100 when you have no real benefit from it, only counterfactual benefit, an example of winning?

No, it's a clear loss.

The only winning scenario is, "the coin comes down heads and you have an effective commitment to have paid if it came down tails."

By making a binding precommitment, you effectively gamble that the coin will come down heads. If it comes down tails instead, clearly you have lost the gamble. Giving the $100 when you didn't even make the precommitment would just be pointlessly giving away money.