Originally Posted by
shady
Yes, they are travelling on ESTA.
Edit: seems only returning Visa Waiver Program travelers with approved ESTA are egible.
I don't know what CBP means with that wording. I suppose it could mean you can't use MPC for the first time you enter the USA but that's just a wild guess.
To answer your previous question about kiosk vs officer --
Think of it as "both". Your phone acts as the kiosk but then you bring it to an immigration officer.