A threat to email? I'm not convinced.
However this is a good try to make Twitter more relevant and to bound users stronger to the platform.
I can see some usecases not even for private stuff, but also for commercial purposes. It could be THE service platform for companies. At the moment quite some companies offer great support via Twitter, but mainly in public posts. With that 140 char limit blast away and the easy adding of photos, it might be an alternative to other private support systems.
Not only that, users can communicate now within the platform without leaving the app or the website for quick private messages with more content.
So, potential is there, but do users accept that with email, Facebook, Hangouts, and other proprietary chat apps?