There's very good reason for that : this law is yet another example of the EU's new favorite tactic: laws without the justice system.
The ONLY person that can use this law is the EU executive (commission). They get to sue, essentially any site they want on the internet. You, EU citizen or not, do not get to sue anyone else, no matter how much copyright infringement, how much damage. You can politely ask the (no doubt up to 10 person) EU agency that the commission puts in charge of this law, but that's it.
The EU commission is not just the only party that can use the law, they are also arbiter of this law. They never have to build a case before court, and of course in practice this means you're declared guilty and punished before your first chance to see a court.
In other words: they can prevent any site they like from getting sued at all and they can sue any site and convict. Then you can fight that decision in court (after, of course, penalties are extracted). In court, you start from an extremely disadvantaged position: you have been tried and found guilty. Effectively, in court you only get an appeal option.
I mean I know the EU is a dictatorship (because the both the positive and negative legislative power is in exclusive hands of the executive alone, the EU commission and council: they can enact any law they like with or without parliament approval and they can prevent any law from becoming law, no matter how much parliament wants it. Or they can change it at will, or ...
But this is even worse than that. This law does not just give them dictatorial power, but essentially makes them an international public prosecutor for internet sites, who does NOT report to any elected government (only reports to the commission which is not elected).