Your video clip is a joke. It's a visual pun.
Wendy's definitions are correct.
I can't hear the sound in this video clip.
In this video clip, there are no "doormen."
In this video clip, we see two "door-to-door salesmen."
There are very few door-to-door salespeople in the U.S. any more, but in the past they were typically selling things like brushes, magazines, vacuum cleaners, or encyclopedias. I believe Avon and so others still sell cosmetics that way.
You could speak of a "door-to-door vacuum cleaner salesman" or a "door-to-door encyclopedia salesman."
The joke here is that they are selling DOORS. So, they are "door salesmen," they are "door-to-door salesmen," and they are "door-to-door door salesmen."
However it's a fairly silly joke because nobody sells doors that way--and if they did, they wouldn't use a full-sized door, they'd bring a catalog and perhaps some miniature door samples.
It sounds from your description as if they take the joke to another level--one of the salesmen is a door-to-door door salesman, and the other is selling SALESMEN. Specifically, he is selling a door-to-door door salesman. Hence--using brackets in the style of a computer language--he is
"a door-to-door [door-to-door door salesman] salesman."
Sounds like the kind of humor Lewis Carroll, author of "Alice's Adventures in Wonderland," might have enjoyed...