Are you sure it is a Leslie Rotary speaker?
I have never played through a real Leslie Rotary speaker (so what do I know) but the oscillation rate on that sound in the video seems pretty fast. Can a Leslie Rotary speaker rotate that fast?
Plus, there seems to be almost a "wah" type of affect. Could it be a phaser? I have played phasers that kind of sound like that.
Either way, it sounds pretty cool. I had forgot about that song. I think the last time I heard it was on the Simpsons when Homer lost Maggie when he was baby sitting her :-)