I would say that video has a mixture of correct and incorrect information (and again this is my interpretation of UK law, as someone that doesn't work in the legal realm).
Yes, absolutely correct that as a player you are not breaking any laws at all. However you are breaking TOS and as a player you could be banned from retail servers if they KNEW you were playing on private servers. No, I doubt they would want to do that though.
By and large the source code to WoW server emulators are free from server material. The grey area comes in two parts. First, is information that is reverse engineered. That is packet IDs, server side spell scripts, boss scripts etc. In general so far UK legal cases have hinted that this is also OK, in other countries this might not be the case though. The second grey area is the world server database. That is information about all the creature locations, paths, quest information etc etc etc. That is all server side information, gained either manually by observation, or automatically based on data mining/connection sniffing, this could be argued to be IP. That grey area COULD fall onto Blizzard's side. It's not clear, I'm not aware of it being tested.
The part I call absolute nonsense on is when he says a policemen has to tell you when you're in trouble like this. No, that's far far from the truth. Unless they NEED help from the police to identify you, this is an entirely civil affair. That is, Blizzard would be funding the case against you, it would be a criminal case but not funded by the police or CPS. So, there I call nonsense. The police don't need to get involved at all here.
In the end, in the case of Nostalrius. If I were running a server and I received a letter addressed directly to me threatening legal action, I reckon I'd fold too, since I wouldn't have the resources to defend such claims. As it is, I know being based in the UK I'd be putting myself too open to risk in running a server anyway. Hence I don't

Casual and proud.