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If their website is accessible from the EU then they are subject to GDPR.

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.

Not only do they take subscribers, they actively target the European market. When I open nytimes.com, a pop-up offers 0,50€/week digital access.

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.

The EU says that GDPR applies globally.

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.