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I'm pretty sure they are doing image tracking. They speak about being able to frame the image you want before, and the drone keeping that framed:

We have designed our drone specifically for action sport, on the tracking mode we offer framing is more than just follow me: it allows you to set drone position relative to you (altitude, distance, orientation), so that you can get perfect aerial shots.

Phone sends GPS coordinates to drone.

Just guessing: it follows your phone?

How, technologically speaking? GPS is way too coarse for what they're showing.

Dead reckoning of phone trajectory using inertial sensor (of the phone) + gps corrections ?

I don't see a dedicated camera on the drone (using gopro for machine vision is not ideal), nor a beefy cpu to handle person tracking onboard, but I could be mistaken.

You can get centimeter accuracy with gps. http://swift-nav.com/piksi.html Even with cheaper modules and phones that dont carrier phase rtk, you can get meter which would be plenty for this application.