The concentric rings of increasing blurriness remind me of a Fresnel lens. I'm no optician and always found the physics of light rays confusing as heck so the only words I understand from the wikipedia aricle are "A Fresnel lens can be made much thinner than a comparable conventional lens, in some cases taking the form of a flat sheet." Maybe someone else can tell whether that's what's being used here? https://en.wikipedia.org/wiki/Fresnel_lens
The article says that they're biconcave, which means that the thinnest part of the lens is in the centre (similar to a red blood cell). For high-myopia lenses, they often remove the lens material away from the centre to limit the maximum thickness at the expense of reducing the field of view. The resulting surface is usually left unpolished, but the lens underneath will still bend light, resulting in the circular patterns you mentioned. In this case a very large amount of material is removed as they would be impossible to use with a conventional frame otherwise. The alternative would be to use glasses with very small lenses.
I don't think it's a Fresnel lens. Fresnel lenses have rather obvious rings and have poor optical qualities for most applications besides light sources, cheap slide projectors, and magnifying glasses.
Here, the "lens-within-a-lens" effect that you see is because, generally speaking, myopia lenses shrink the image. But this lens is so extreme that the image is shrunk into a small bubble in the middle. The ring-like structures around this bubble are due to internal reflections within the lens.
