Ok, I'm all choked up. I programmed 5-axis Mats for 7 years doing airfoil work. By the time I changed careers the controllers were getting powerful enough to do B-spline interpolation right on the machine; machines in the past could only do point to point and circular arcs; The CAD system would output "knot points" of the spline and the controller would do the rest.
Seems like this vid is a marketing one; 5 axes of simultaneous motion is only done when NECESSARY; very hard to make cutter offsets when the part is "all over the place"
I still remember Boyd Coddington, I think it was, when asked how he made a mirror for one of his award winning street rods from a billet of aluminum - "take a block of aluminum and cut away everything that doesn't look like a mirror". I guess this is the same principle, refined a bit?