For this specific case, Texas laws prohibit overall the use of public roads for takeoff, still a municipality may issue an ordinance to allow some takeoffs from county roads, describing the specific procedure to be used.
The question boils down to whether such specific ordinance exists for this takeoff. A quick search on for the aircraft tail number and Chambers county ordinances doesn't return anything as of today. It's an offense unless specifically authorized, though the penalty, a fine between \$25 and \$200, doesn't seem to be a real deterrent.
FAA doesn't regulate off-airport operations
Private helipad in Oregon, source. Go there with Google Maps
Other entities can regulate or prohibit off-airport operations
The insurance may prohibit operations off-airport.
The State may prohibit the use of public land for specific activities, including for air operations.
Air operations may be prohibited for purposes of noise protection, natural world protection, etc, so that one's hobby doesn't prevent safety, peace and quite for others.
Whether taking off from a highway is allowed depends on the State.
Texas and some other States prohibit off-airport operations
Texas specifically prohibits using public roads for takeoff and landing for any flying object, manned or not:
A person commits an offense if the person takes off, lands, or maneuvers an aircraft, whether heavier or lighter than air, on a public highway, road, or street except [...]
Emergency-related landings are indeed never punished and are possible everywhere, and it is conceivable some takeoffs may be emergencies too, but likely not in the present case.
Emergency landing in Texas on Interstate 35, source
Other exceptions must be specifically allowed by a local law maker (commissioners court of a county) using an ordinance:
A commissioners court of a county may enact ordinances to ensure the safe use of county roads by aircraft. An ordinance may:
- (1) limit the kinds of aircraft that may use the roads;
- (2) establish the procedure that a pilot shall follow before using a road, including requiring the pilot to furnish persons with flags at both ends of the road to be used; or
- (3) establish other requirements considered necessary for the safe use of the roads by aircraft.
It's possible the operation you saw had been allowed by such local ordinance.
Some States allow them by default
In contrast Montana allows landings and takeoffs in general, though they are still subject to a procedure:
Aircraft landings and takeoffs from public roads in this state are lawful if proper safety precautions, as approved by the governing jurisdiction of the roads, are taken prior to the landing or takeoff
Fields, Oregon, source. How to get there, including the road landing on Youtube
Of course using a private property is not allowed without prior consent of the owner in addition of regulations mentioned above.
More: Is It Legal To Land A Plane On A Road?