Don't worry about the term, you used it well. The sauna theater is a business like the sauna. In the sauna theater there are big TV screens and Cinema to watch whatever you want while enjoying the saunas. They also have spa area, body waxing, massages, etc....
But in the video they wear clothes and in the sauna or in the sauna theater, you have to go alone with your towel, no one enters with clothes.
And the other issue is that if it is "gay". women do not enter, no way. I've lived in Amsterdam for 1 year and I know how things work there, the spaces are limited, they are respected. So it is only one of those huge sexshops, which have areas of Glory holes, dark rooms, cells, exchange of couples, swingers area, etc... And there everyone can enter regardless of sex and sexuality.
I think in the video the protagonists don't even say where it is.... Or maybe I didn't understand it.