Forget all the stuff out there that says the GDPR protects EU citizens. This is a question of jurisdiction and enforcement. Say I run a blog under a business registered in the US funded by advertisers in the US. A EU citizen that comments on posts issues a GDPR request that I ignore. Their government fines me. I tell them to get bent, I am out of their jurisdiction. What can they do at that point?
Probably nothing.
You would need an international law expert to be sure of the exact consequences, but if you have failed to pay a court ordered file then you would probably be unable to travel to an EU country or a country with an extradition treaty. You would certainly face issues if you ever wanted to expand your business overseas.