I haven't been there, but I've been to Kitt Peak Observatory in Arizona, and the one on Mauna Kea (but we couldn't stay on top of Mauna Kea much past sunset, sadly). Mauna Kea was surreal even during the day because it feels like you are on top of the world.
The most amazing view of the night sky I've seen was at Kitt Peak. It really does look a lot like this video, but not as bright and without all the color. To be able to see the sky like this requires an absolutely dark location, and you will be seeing at the lower limit of your vision. The rods in your eyes are more sensitive than cones, but they cannot see color well or at all.
The times in the video when it looks like the sun came up are actually the moon. With a camera, it doesn't take HDR to be able to see stars at the same time as the moon- just set it so the moon is overexposed and the stars are correctly exposed. With your eyes, though, you won't be able to see that many stars once the moon is out because it will temporarily ruin your sensitive night vision. When the sun actually comes up in the video, everything goes white since it looks like they are using a fixed exposure setting.
Last time I tried night sky photography with a camera, I couldn't use long exposures because even in the relatively short exposure time the stars would move enough to leave short trails. They might have done this video by registering several shots from a short time frame on top of each other. Or they might have a better camera than I do. It would take a fast lens and a sensor with low noise at high ISO settings.
In short, it would be worth a trip to camp there, or somewhere similar. You won't see a bright, colorful sky, but you will probably see at least as many stars as there are in this video. Seeing the milky way at night never ceases to amaze me, and it is sad how little of the night sky we can see in most places because of light pollution.