I’m guessing that they are referring pretty directly to swing dancing , the popular American dance style made famous in the 1920s and popular through the 40s, characterized by a syncopated rhythm, a step where the dancer tends to ‘swing’ out from their partner, and the use of improvisation and borrowing from other dances, and usually based on the Lindy Hop or the Jitterbug. A youtube video showing fast-tempo swing can be found here. Musicals typically employ the leads, who sing and also sometimes dance, but also have more minor rolls for just-singers and just-dancers- the “swing dancers” may have been background characters who had no speaking lines or singing lines, just impressive dance. This is usually done as a sort of theatrical division of labor- lead singer/actors usually can’t also dance- no one has the time to do that kind of triple-training.