In short
You can look at another video on which the same aircraft is refueled at Saranac Lake, the destination airfield of this trip. The refueller employee uses tank necks on top of the wing:

The aircraft was also refueled at the airport on your video and before starting the engines the pilot comes check the tank caps are in place on both sides. She stands where the cap is located and uses an inspection mirror on a telescopic pole:

Details
Contrary to many large airliners, the fuel tanks on this aircraft are filled from the top of the wing, like this one which seems to be a Cessna Citation with low wings:

Source.
The filler necks are not self-closing like fuel couplings on larger aircraft. Fuel spills if the cap is not in place.