Very cool. I did some looking. It seems to be a proprietary technology owned by the on company (their logo looks like a lower-case sigma with an upside-down u). It's not the entire show -- the sole is made the regular-old way and the upper is made directly onto it, no adhesives.
The way they make it isn't how I expected. spray-on technology is nothing new. I worked one summer at a place that did spray-on fiberglass -- the glass fiber was fed through a rotating blade, and the resin nozzle was just below it, so a mix of glass and resin hit a mold or form of what was being made. I'd expected that the new thing these folks did was using a type of 3-D printing -- resin sprayed out and turned into continuous fiber by a laser or heat. But they say that they use miles of a single filament to make the outer part of the shoe, implying that there's no liquid involved.
They seem to be saying that there are two selling points: that it's much cleaner and much lighter. I'm not sure I buy that there's a huge difference, since most of the pollution produced in the athletic shoemaking process and most of the weight of a shoe are in the sole.
AFAICT the vast majority of athletes wearing these are runners. Given that the main selling point is the weight, I'd say that is likely to remain the case. As a former sprinter and marathoner, as well as having played competitive volleyball, I can say I was always looking for a light shoe running, but never noticed much of a difference in volleyball, basketball, etc.
