Unless the organ is yours or unless you know what you're doing, I don't recommend opening up the organ and changing things around. It's okay to look and learn but until you feel comfortable making changes, it's not a good idea. Just a suggestion.
Listening to the video, it sounds like the Leslie (which looks like it's been mounted to the wall near the ceiling) is single speed (fast/off) and the organist just didn't switch speeds. I can't hear any rotation at all.