The problem with abiding by European privacy laws is that if you're not European, you don't count. So if you're not European, there may as well be no privacy at all. You're more or less on your own - just the same as with American privacy laws.
If they can prove one end of the conversation is not American or not in the U.S. you're recorded... but because it's so hard to do that on the fly, you're recorded anyway and they'll figure out the legal repercussions later... by hiding it, diverting the question or flat out lying about it.
It's a shame, this looks on the surface like a great product. But I agree with the point made earlier: In the age of Snowden, statements as vague as "Wire interactions are secure and we comply with European privacy laws and regulations." aren't enough for anyone to stake their security on.
The fact is, when it comes to communication security, the Government has proven themselves untrustworthy too many times for us to believe them anymore. Once could be written off as a mistake, twice, perhaps oversight wasn't good enough. But three, four, five times... the fact is, Governments have torpedoed any reasonable person's ability to trust them when it comes to looking after their privacy. So saying that you "comply with privacy laws and regulations" is no comfort. In today's political climate, if you want the trust of the people, you need to go above and beyond in the name of the people.
Probably more than US laws anyway.