"We don't know who did it but when found they are liable for X€ of damage"
Apparently the answer is that you can sue a web site and serve the Internet service provider and whoever registered the domain name.
I would imagine that if there's an anonymizer for the domain they are accepting responsibility for delivering such subpoenas. (I didn't see that started as fact.)
Googling turned up that this happens a lot in hit and run cases. I didn't go down that rabbit hole.
Is it because this is an injunction rather than the outcome of a trial? But I thought an injunction could only stop behavior, not order a fine.
Or does it have something to do with it being a corporation rather than a person? Or with being a (presumably) foreign corporation?