What is the difference between their view of themselves and what we read in the history of what German children were being taught about their Aryan superiority under the “Third Reich?”

Not much, except two things.

1. The Third Reich held that view for about a decade before its collapse while the Chinese have clung to it since the Qin Founding, and the Proto-Chinese before Qin held the same view since the Zhou Dynasty.
2. The Third Recih believed they were superior because of the German culture. The Chinese define their culture as superiority. In other words, in the Third Reich German culture produced ethnocentrism as a nasty side effect. In China, millennia of ethnocentrism have spawned a culture as a side effect. As I've written before and quoted ad nauseum, the Chinese want so badly for you to know how ethnocentric they are that they enshrined it into their name.