This is an amazing video! I've seen quad line kites, but I've never flown one. Quad line kites have four (quad) lines attached to them, on the top and bottom of the right and left sides. They attach to handles like so:
The beauty of quad line kites is that they can hover, back up, spin in place, and do other amazing tricks. If kites were birds, they'd be the hummingbirds of the species. Very expensive hummingbirds.
I never would have thought to combine kites and skating. This couple makes it look so effortless. If I could stand up on ice skates, I'm sure I'd end up tangled in the lines, the personification of Charlie Brown's kite-eating tree.