Scattter? not so much.
Moth eye antireflection coatings use very small structures (smaller than the wavelength of light). They don't scatter light in some benign direction; they don't reflect it at all (ideally).
Moth's eyes don't do this. The name comes from the appearance of the structures as seen with a scanning electron microscope; they resemble the compound eyes of moths. I believe that moth's eyes are highly reflective, but as retro-reflectors: they send the light back to the source.
That type of AR coating has been around for a long time. The earliest AR coatings, developed in the 19th century, involved "staining" glass chemically. It doesn't give a regular structure, and it isn't simply a surface pattern, but the effect is similar.
The advance here is coming up with a plastic film that could be applied to a screen, rather than patterning the glass directly (expensive).
And, yes, you wouldn't want to touch such an AR coating. Fragile, and difficult to clean without damage.