Apple's saying that the import ban will hurt them in ways that can't be fixed, and so it makes sense to stay it until their appeal decides what's going to happen. It's why this stay is only for ~2 weeks, because that's all they think is needed to get to a more-permanent decision from the appeals court.
The idea is that harms that can't be fixed (by e.g. ordering someone to pay money) should be avoided until the system has settled on a definite answer.
> I’m not sure I understand why third parties are still allowed to violate a ruling, either.
The ruling is just blocking imports, not sales. I don't think that Apple is actually required to freeze its own sales, per se, but they're very just-in-time for stock so it was an effective ban for them unless they wanted to stockpile.
Third parties are thus able to sell through whatever stock they have.