In the typical web/e-commerce context someone whose IP address geolocates to an EU based end point or someone who lists their delivery address as inside the union.
The problem is that the law applies to them even if they use a proxy. If they report/sue you afterwards, you might be looking at a huge amount of trouble.
That's not very comforting when your goal is avoid having unforeseen problems like being arrested on your European vacation due to violating a law that doesn't apply to your country but you still violated because it applies to all EU citizens regardless of their geographical location.
The general direction is correct, but not the specific implementation - since it applies to everyone in the EU, no matter what their citizenship, you can just reject all transactions where the shipping address (or credit card address for virtual goods) is in the EU; and that should probably be fine.
On the other hand, if you actually want to sell stuff to EU and get a nontrivial number of deals, then no amount of weird checkboxes is going to convince the regulator that it's okay, they aren't stupid.
