I had a closer look at the stars and unless I made a mistake with timezone conversions, or my planetarium program messed up somewhere, I believe it is more likely that the video was filmed an hour earlier than stated, at around 9:20 pm local time instead of 10:20.
This is a crop of the lower right part of the video, with three stars labelled.
This is the same crop, overlaid with a corresponding simulated view of the sky from Cape Hatteras, on Jan 7 at 21:20 local time.
Centered on Pi Puppis, a close enough match I would say despite slightly different scales (I did my best, hah!) and alignment issues due to the horizon not being perfectly level in the video. Note especially the angle between Pi Puppis and Nu Puppis.
Now take a look at the same crop, overlaid as before but with the simulated view from an hour later, 7 Jan at 22:20 local time.
Note how the angle between Pi Puppis and Nu Puppis is radically different.
If someone could confirm this, that'd be nice. As I said, I'm not entirely sure I didn't make a mistake somewhere along the way.
For what it's worth, if this really was taken around 21:20, that would put it 5 - 10 minutes past the launch of SpaceX's Turksat 5A mission. This is a screenshot from the webcast showing the trajectory. If I had to guess I would put this image a few minutes past the object's appearance in the video.
It is quite some ways from the camera's location though given its easterly heading. Launches into an ISS-like orbit head out to the
NW NE, much closer to the eastern seaboard. Maybe some could make some calculations on how far above the horizon the rocket would have appeared from Cape Hatteras? I haven't got the time right now to do so myself.
EDIT: If you want to know how high above the horizon the object was in this crop, it moves past Nu Puppis, which was at an elevation of 6°12" at 21:20 and 9°58" at 22:20.
EDIT2: Actually, I'll do one quick calculation. I measured the downrange distance between Cape Hatteras and the launch trajectory as about 750 km / 465 mi by the time it would have entered into the camera's view. To appear 6° above the horizon, it would have had to be at an altitude of about 125 km / 78 mi. According to the info in the launch webcast, the rocket passed this altitude 4:15 min after launch, or at 21:19:15 local time.