I'm not really an expert when it comes down to how private servers actually work (client/server side thing) so thanks for the insight. Now for the dumb question: I assumed developers actually developed the client or modified an old version of WoW in order to run a vanilla private server, no? If that is the case, it looks like a quite clear infringement of copyright law because they would have used and redistributed the game without asking Blizzard first. Even if they really wrote every single line code themselves, they would still be using music, images, database, etc. (remember there is also a generic category for whatever doesn't fit the most common ones).
As far as images and music go, I'm not sure people have to actually download to or stream on their PC to qualify for redistribution (which only matters if it's not for private or family use), making them available without Blizzard's consent may be enough. Perhaps, it would be akin to using songs in TV commercials: ad companies need have the copyright owner's permission to play its music, even though the public don't really download/stream anything... the music is just made available to them.
@Sidious78 : I didn't open up the can of worm that "not making money" is, because the Private Server We Cannot Name is a borderline example imho. They claim it was to pay the ISP and that everything else went to charity but a) that's still making money and b) it is their word. Also, I brought up French law because that particular private server was hosted in France (if I remember correctly). The EU only has directives and basic rights (plus well, jurisprudence from its Court) which member States have to enact into their national laws. Generally speaking, the main difference is whether a State considers video games to be "multimedia work" or "computer programs" : in the latter case, they recognize all the different aspects of the game (code, music, images, etc.) and protect them all separately while the multimedia approach considers game to be a whole. In that case it could be harder to prove copyright infringement when not everything was copied (ex. the code re-written). Not sure if Blizzard would need to prove that all of it was stolen (as a whole) and not just a parts of it, though.
Since some people think Russia is a safe haven, just know that Russian copyright law is actually stricter than France or EU. Video games are not exactly defined, so they can be considered both computer programs and audiovisual work (so the multiple protection, like France). On top of that, Russian law also protects individual parts of the game. The name of the game, characters names, set-ups and graphics can be eligible for copyright protection. A few years ago Russia even set up a specific Intellectual Property Court because of so many disputes around copyright, with the purpose of adhering to international standards. Thus, I wouldn't go as far as assuming that because Blizzard is a U.S. company then Russian courts won't do their job. Seems a far cry to me.
Maybe when video games will be better defined by copyright laws and there will be more precedents, Blizzard will feel comfortable to sue. Ambiguities can be a real problem when they risk to lose parts of their IP because the law is not up with the times yet.