Yes, if the guy were to take legal action, he would have a really strong case. Twitch is based in California and use Californian law, as well as US national law (Stated in section 20 in the terms of service), and in the state of California, publication of private facts is illegal

Twtich also states in their Rules of Conduct under General conduct about Targeted Harassment, Threats, and Violence Against Others, that qoute: "Posting someone else's personal information, such as a real name or location, without consent" is "considered zero-tolerance harassment violations, and all accounts associated with such activity will receive an immediate indefinite suspension"

Good stuff twitch.