In the case here, Epic doing a behavior to go around a store policy that EU specifically is considering bad may mean they cast aside the US rulings.
From there a lot of things can happen to negotiate a resolution, such as negotiating penalties for not following said contract.
I don't think Epic will be able to convince a court that there is no resolution when Apple has already said before and now what they would require for Epic to resume their business relationship with Apple.
The EU is a sovereign entity, enforcing its own laws in its own territory. A US court ruling can't compel the EU to allow Apple to violate EU laws when operating in the EU. How would that even work?
In a word: treaties. Usual disclaimer that I'm not a lawyer yada yada, but treaties are generally why one country's laws or legal proceedings might affect another country in some way. Think stuff like US copyright law being applied to Europe [1]. I don't actually know how or if anything would even apply in this specific scenario (not a lawyer and I think it's pretty unlikely that the US court ruling would affect the EU DMA here), but treaties are what you'd look at to find out.
[1] Technically those countries passed their own versions of the US law, but it's all hammered out in the World Intellectual Property Organization Copyright Treaty.
Remember that the whole goal of the DMA is that actors like Apple and Google can't decide to block competiton on a whim, the exact thing they are doing right now.