My initial thought is this is working via the microphone/speakers on the computer and phone. My second thought is if you don't need to unlock the phone and activate anything I bet this absolutely kills your battery life.

I'd bet the proprietary technology is that the phone constantly emits some tone outside the normal range of human hearing (probably with some time varying value encoded in the frequency of the tone) which the mic on the computer listens for. Once the computer picks up the tone, it decodes the time varying value from the tone and from there proceeds like any other TFA login system.

There's also a question of what happens in a busy setting like say an office environment when multiple people are using this system and say two people attempt to login to a site secured with this at the same time.