I believe there is deeper subtext revealed here by Kubrick related to the tensions between petite bourgeois morality (and "Dr. Bill" is solid Upper East Side petite bourgeois) and the moral position held by "Hungarian" aristocrats who may or may not wear red robes while playing Grand Master in a ritualized ruling elite social gathering.
A tearful and oddly emasculated "admission" by Dr. Bill follows.
Because I took the mask to mean the wife participated in the orgy, so the rest follows accordingly
Compare the Dr. Strangelove cover which shows the round table in the War Room [1]. If you squint, you'll realize what you're looking at is actually a mushroom cloud. The table is the main part of the mushroom cloud, the men sitting around it are little explosions at ground level, and the circular light above the table is the ring around the mushroom cloud. This is obviously intentional, but there's no implication that a nuclear bomb literally exploded inside the war room.
[1] https://img.goldposter.com/2015/04/Dr.-Strangelove-or-How-I-...
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]
[0] https://en.wikipedia.org/wiki/Room_237
[1] https://en.wikipedia.org/wiki/The_Shining_(film)#Social_inte...
[2] http://idyllopuspress.com/idyllopus/film/shining_toc.htm
> “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.