Minor lawfagging:
He's right about the contract. If she made the offer and he accepted in writing (doesn't have to be in writing, but writing is always more provable) then he can sue for specific performance. A judge would basically say Pelosi has to follow through with her offer and allow the speech to go on unless she can cite some kind of force majeure to get her out of it, but i don't see that happening. I don't know if the fact that the plaintiff is the POTUS makes a difference, but I don't think it really does.
Donny knows contracts and she signed one when she made the offer, thankfully in writing. Trumps tweet says he responded in writing, which means there is a contract in place and it doesn't matter whether Nancy knew it was a contract or not. Trump can sue her, as he alluded. Specific Performance is when you get a judge to say that some specific event should take place, as per the contract that was violated. Like if a singer sues a stadium because the stadium cancelled a show for no good reason, he might sue the stadium for specific performance and the stadium would have to let the show go on like they originally promised.
A major lawfag could probably explain the nuances about how it might look different if the POTUS is the plaintiff, but it might not be different at all, I don't know.