Wow I would love to learn the details of this technology.
The secure chat protocol they're using is something they developed and haven't yet published. It sounds as if it's similar to OTR, though. TextSecure (an encrypted SMS app I work on) uses a version of OTR adapted to the mobile environment, which is documented here:
Check out this video which attempts to explain this type of encryption: http://www.wimp.com/howencryption/.