In a way, yeah it is a better spring steel. Many shape memory alloys, besides their famous shape-changing-under-heating behavior, can also have superelastic properties, meaning they can reversible handle much larger strains than typical alloys (by a reversible phase change in the material). This means they can work as a better spring alloy. https://en.wikipedia.org/wiki/Pseudoelasticity
Nitinol typically has tight compositional tolerances and is used for things like stents and catheters. It's nothing new in the medical field. But it'd be pretty damn impressive to manufacture something so finely structured out of nitinol at scale.
I wonder, though, if the rubber can be more rugged as a result.
Materials/chemistry is so far out of my wheelhouse, I can't even imagine what that might be. But I'd imagine there might be a way to optimize the synthetic rubber for handling friction against the road surface while not having to optimize it for handling pneumatic pressure.
Unfortunately, I suspect that the things done to make the tire survive road friction better also make it grip the road worse. And that there's likely not a chemical formula that one can apply which wouldn't work equally well under a pressurized tire... but hey, most things are evolution, not revolution, anyway, right?
I could see these being much better for mountain bikes than for road bikes as the woven surface might actually improve traction on mountain bike trails.
It's also kind of funny that they admit they'll have to wrap the metal in a rubbery substance for traction.
So we're pretty much back at steel radial tires.