Simple to actually do the geometry. Watching the video, it is pretty clear that the moon is in its first quarter and the sun is getting low in the sky. Using the animation presented here:
https://www.khanacademy.org/partner-content/nasa/measuringuniverse/spacemath1/p/animate-phases-of-the-moon you can get a relative position of the sun, moon and observer on the earth, as pictured below (not to scale). Note that the red dot is the observer who is on the surface of the earth and about to rotate out of the sunlight and into the dark night. If you were standing where the red dot is located, the moon would be overhead and the sun would be nearing the horizon in the west, just as the video showed.
Now get a very long roll of paper, and recreate the modeled positions of the earth, moon and sun as shown below, only this time draw them all to scale. So let's say you draw the earth as 1/2 inch diameter circle. Then the moon would be a circle about 1/16th of an inch in diameter and it would be located about 15 inches below the earth on the roll of paper.
Now to draw the sun on the paper to scale, you would need to unroll the paper so that you can draw a 4 and 1/2 foot circle or at least the partial circumference of that circle 484 feet away from both the earth and sun. Now draw the lighted and dark areas onto the earth and moon. so that the dark areas are opposite the sun that is 484 feet away on your unrolled piece of paper. You will see that the dark areas are in the exact positions as shown on the not to scale model depicted below, which also just happen to match what the maker of that video observed: the dark area of the moon was facing to the east and the moon was pretty much overhead, while the sun was low in the sky to the west and about to set.
It naturally is hard to visualize such extreme distances, but this is actually simple geometry. It is just extreme in the sense that two sides of the triangle between the sun, earth and moon are both about 93,000,000 miles long. The sun is low in the sky because the earth is rotating away from it, but the moon is up there high in the sky with the sunlight that is striking it from the west....but from a very great distance.
Here is a fun attempt to demonstrate the scale of our solar system in a way that we can start to comprehend the extreme distances involved, compared to the scale of distances we normally encounter on earth:
https://www.washingtonpost.com/news/speaking-of-science/wp/2015/09/18/this-scale-model-of-the-solar-system-is-truly-mind-boggling/?utm_term=.e00985163f99And here is the NOT to scale model of the earth, sun, moon and observer (red dot) as they would have been located in the video: