"The Shining" is, among other things, a giant metaphor of human (and in particular, western) civilization. The constant references to the moon landing (and 2001: A Space Odyssey) can imho be understood as an one of the many illustrations of the great and unprecedented things that came out of a civilization that is masterfully portrayed in the movie as a fading grand hotel built on a burial ground that is trapped in a seemingly eternal winter. Seeing it as Kubrick's confession that he staged the moon landing is not only silly, it doesn't even begin to describe the film's poetic depth. However, I watched the documentary where this clip is taken from (Room 237 [0]) and can recommend it with reservations. But I remember that it "jumps the shark" somewhere around the middle of the documentary.
Just to elaborate: I often hear people discredit "The Shining" because it didn't scare them enough, or because they think King's book is better, or because they find Duvall's and Nicholson's performances over-the-top. In my opinion, "Shining" is Kubrick's masterpiece. It is arguably deeper than 2001, has a very high artistic quality (some scenes are staged like a ballet) and at the same time, the movie is constantly entertaining and thrilling (which is a quality 2001 clearly lacks, as I have experienced again and again when I tried to watch it with friends who were unfamiliar with Kubrick's work).
If you want to go down the rabbit hole of "The Shining" interpretations, you should start with the Wikipedia article [1] and end with the shot-by-shot-analysis [2]
It's an excerpt from a feature length documentary called Room 237. Taken as a whole, it's a pretty fun, non-judgmental tour through some colourful interpretations and theories surrounding Kubrick and The Shining. I don't think it's actually intended to convert anybody to moon landing skepticism.
> “I stood staring at all that stuff for weeks while we were shooting in that room. It’s a downhill skier. It’s a downhill skier. It’s not a Minotaur.”
Etc, etc. Room 237 is not only the ravings of madmen, it has a bit right st the start where a guy is talking over The Shining shots, a baby starts crying on the background (of the guy talking) and they stop and discuss that. I turned it off in disgust after that.