The elephant in the room is the FAA. They either approved this tether system, or did not monitor this operation since they openly advertised the use of the system. Should be interesting.
The FAA only requires you to wear your seat belt for take off and landing. It is my understanding looking at all the videos and dialog that standard seat belts were worn during take off and I assume landing. Once airborne, they can take those off, and there is no further requirement until landing, therefore the harnesses are a bonus and do not need to be approved as I am guessing they are attached to he hard points on the floor.
The rules say nothing about once airborne.
14 CFR 91.107 Use of seat belts
Highlight added by me:
Sec. 91.107
Use of safety belts, shoulder harnesses, and child restraint systems.
(a) Unless otherwise authorized by the Administrator--
(1) No pilot may take off a U.S.-registered civil aircraft(except a free balloon that incorporates a basket or gondola, or an airship type certificated before November 2, 1987) unless the pilot in command of that aircraft ensures that each person on board is briefed on how to fasten and unfasten that person's safety belt and, if installed, shoulder harness.
(2) No pilot may cause to be moved on the surface, take off, or land a U.S.-registered civil aircraft(except a free balloon that incorporates a basket or gondola, or an airship type certificated before November 2, 1987) unless the pilot in command of that aircraft ensures that each person on board has been notified to fasten his or her safety belt and, if installed, his or her shoulder harness.
(3) Except as provided in this paragraph, each person on board a U.S.-registered civil aircraft(except a free balloon that incorporates a basket or gondola or an airship type certificated before November 2, 1987)
must occupy an approved seat or berth with a safety belt and, if installed, shoulder harness, properly secured about him or her during movement on the surface, takeoff, and landing.