Actually, I think I have a possible explanation from a globe perspective for the sliver of light on the underside of the moon, but I haven't thought it through fully yet. Nevertheless, I'll post it here, but first, kudos to Blorgon A173 for that information he/she gave on 5/11/17. Anyway, the moon takes ½ month to make a half-orbit around the earth; whereas the earth takes only 12 hours to make a half-rotation, so, in the video, even though the moon appears to be moving downward, because of the earth's spin, the moon is actually moving upward, but at a slower speed, in the view of someone on the earth, than the earth is spinning, so the moon actually seems to be going down, merely because of the spin of the earth changing the view of the sky faster than the slower motion of the moon going up. In fact, at the same time of evening on the next day, it should be higher in the sky. Because the moon is actually going up, the sliver of light on the bottom of it is obscured by the earth from the top going down. I have tried to make a rudimentary illustration below, but I haven't really bothered with figuring out the scale.