Plus, the petroglyphs to me only have a superficial resemblance to the old Chinese writing.
And if Chinese did arrive at that time, why would they try wandering around a desert? No horses in North America at the time.
I’d enjoy seeing some kind of ancient wreck evidence, to establish that they had a seagoing tradition (trade, exploration, power projection). Of course, the Japanese used to have a floor date beneath which human presence in Japan was not permitted, analogous to the Clovis-first in the Americas; after the oldest *possible* remains were found, the digging stopped. Some maverick decided to keep digging and discovered that Japan’s prehistory didn’t just mysteriously fire up during the Neolithic. :’)
As to why would the Chinese be wandering around a desert, the question is how close was this petroglyph location to a navigable body of water? Most of the sites that Gloria Farley studied over 30 or 40 years were located relatively near rivers and large streams that ships and small boats could travel on. It might be that a number of marks by various exploring cultures were made when the point was reached that they could no longer go upstream, kind of as an explorers flag to claim the discovery or voyage.