If you conduct business (even if only over the internet) in the EU, the EU considers you subject to their laws. Same as with the United States (and probably every other jurisdiction).

Do you have to comply with EU law if you conduct business there? It depends on whether the EU can enforce judgements against you. If you live in the EU, then the EU can certainly enforce judgements against you. If you live in a cooperating jurisdiction, like the US, then I'm pretty sure that EU judgements can be enforced against you. That would take more effort on the EU's part, but if they really want to, I believe they can ask and get the US courts to enforce judgements.

If you live somewhere where the courts will not enforce EU judgements, then yeah, you don't need to care about EU laws. At least, until you travel someplace that does...