Flight duration is always about weight. The less mass you are suspending in the air, the longer you can do it with a given amount of power. But obviously that is balanced by the amount of energy you are lofting, the amount of thrust you can generate from it, and at what efficiency.
The video awkwardly described the relationship between energy, thrust and efficiency, emphasizing the benefits of using higher voltage to reduce current for the same watts. But the information in the video was all entirely valid. A larger prop will produce thrust more efficiently, and higher voltage, correctly applied, will supply the needed power for longer, provided each component is correctly engineered to do it. Not every motor will run at 4S+ LIPO voltages, nor will they all drive a large prop without overheating.
The video was geared towards long flights for close-range video capture. If your mission is long RANGE, the recipe is complicated by the need for longer range control, which probably means moving to UHF.
If your goal is long flight times, you're probably looking at a frame larger than 550, so most DJI platforms are off the table. If you're willing to jump through a few hoops to get 15 minutes in the air, then DJI models are fine, but today, long flight duration is really north of 20 minutes.