My guess is that each of the four panels is a half-circle of firmly-woven lightweight synthetic (probably poly) fabric. The borders are not ruffles, but flounces with the same curve as the rest of the skirt. I'd hang the main skirt for a week or more, then trim to fit, then add the flounces.

My guess is also that the swirl segment has been electronically slowed down in order to show the step more clearly.

We made some similar ones for a troupe number. We used 1/4 circles and I believe we used 6 (may have been 8). Unfortunately, my skirt died and has been repurposed so I can't tell for sure.

I made a big gypsy skirt (there are photos in my profile), I used the free circle skirt pattern on shira's website:

www.shira.net/make-cskirt.htm

I made 3-panel circle skirt, it's very big and swishy. The skirt fabric is a light satin brocade. If you're adding flounces to the skirt (there are two on mine) make the skirt a little shorter allowing the flounce to take up the additional length. I think I cut my skirt about about 8- inches short. I That's about how long my bottom flounce is ( which I made out of satin) the top flounce is abut 4 inches in width and made from a metallic lace fabric. For the flounces, I think what I did is got about 2.5 yards of the satin for the bottom flounce, and then cut 9 inch strips and sewed them together end-to-end to go the length of the skirt hem, I gathered the flounces and then sewed them onto the skirt. And I think it took about a yard or so for the 4-inch flounce. It's not super difficult, but it's a lot of fabric.

Good luck!