If someone walked up to me and said that I would start a discussion about some wierd properties of rocks on a different planet, but it would up talking about meteorite impacts, I would have laughed. Yet, here we are, dicussing it! Oh well, never mind.
I think this idea is very interesting, and well worth investigating.
The crater doesn't necessarily need to be eroding away, since it is in a dry desert. The Nazca lines, after all, have survived when they would otherwise have disappeared long, long ago, since they are much shallower structures than an impact crater/basin. Thus, the rings could be very old, perhaps even dating back to the formation of the planet, when such impacts would be quite frequent. And perhaps those mountains are closer than they appear to be, so they could in fact be quite small in comparison. The certainly seem that way in the photos Ainia provided.