It does if they take subscribers from the EU (or california) and apply this process to them. It's incredibly straightforward. If you do business in some jurisdiction, then that business is subject to the jurisdiction's laws.
Hmm, it seems I was wrong then. I had thought that they didn’t localize to any EU countries, but I guess they have more of a global market than the other papers I am more familiar with.
Some violators might successfully keep their assets out of the reach of EU enforcement, but that's going to be really tough to do for any large business with global operations.