Annas archive is not based in the EU (sorry for being not clear). So the law in EU is limited to enforce a ban. In germany it is already "banned" via ISP but just DNS.
But the real servers are hosted in kazachstan or russia I think. And they do not cooperate so much with EU courts.
So unless the EU installs a great firewall like china, they cannot really shut it down.
Presumably the opposing party is residing in non-US-or(and? depends on the order of evaluation)-EU territory, but I might be mistaken. "They" refers to both sides in the parent comment.
Perhaps I misunderstood something, but according to my understanding
1. Spotify is registered in Luxembourg and has its operational headquarter in Sweden (Stockholm). Both are EU countries.
2. I guess it won't be Spotify that sues, but the individual music labels (very likely united).