Yes, although the video didn't go into it, you can see when they open the app that one of the selections is "Remote shooting". When in that mode, you can change camera settings (ISO, SS, aperture, etc.), focus by touch, and shoot from your phone. You can set it up so no files are transferred, so they stay on your camera for later download.
As for WiFi, you only need the phone and camera to talk to each other. It's basically a wireless tether, so no need for the phone to have any other connection.
Newton
