Thank you for the links! I kind of expected a machine with 10+ floppy slots (: I think I just wasn't really aware of the year this machine was produced.
It is at about 1:47 into the video. It is the same machine shown in that LOGiN magazine article. This one appears to only support the 5 1/4 inch floppies, since I think the 3 1/2 inch disks weren't around at the time, so they must have got a newer machine later on.
Ken's title for the video claims it was from 1983, but from my research, I think that a September 1982 date is more likely. The whole thing is an amazing video actually. Well worth watching. Incredible that it actually survived and is now preserved on Youtube.