Create a very tall composition. Put that composition as a layer in another composition, animate its Y position. Create an adjustment layer which has applied the Polar Coordinates effect. Done. Additional distortions such as the wobbling in the clip can be created using Turbulent Displace and similar effects.
I don't know. It doesn't look like Polar Coordinates. Maybe on the background, but definitely not on the animated figures. Polar Coordinates would heavily distort anything that got near the center of the image, and I just don't see that happening.