I didn't read the article but I assume the ultimatum consists of "I'll cooperate x% of the time if you cooperate 100% of the time. Otherise I'll defect 100%".

Normally in game theory, such statements are not seen as "credible", i.e. you assume the other person is bluffing and you go on to defect 100% of the time.

Maybe you should read the article?

Ok, I did, and it's pretty much it. Punishment is less severe.

Prisoner's Dilemma is about cooperation. "How much do you trust this person"

Ultimatum Game is about bargaining. "At what point are you willing to pay to punish someone for an unfair deal?"

Still processing the paper, but the implication here would be that you can link the two models, but the payoff to doing so critically depends on how much the dominant player is capable of modeling the other player's mind.

Aka smartest model/strategy/robot/person wins.

It's evolutionarily favourable to accept the ultimatum. They claim that if you have theory of the other players mind you should reject the ultimatum and hope the other player gives you a better deal. Giving you a better deal isn't possible in the original ultimatum game, but this is more of an iterated ultimatum game.