Actually, I think Hitler and the Nazis understood that quite well. They wanted their people to strive towards the ideal and help one another, and they wanted other cultures and races to do the same in their own countries, and not in Germany. Hitler and Leon Degrelle have certainly said as much.
This is patently wrong in several ways:
1) Nietzsche did not want "his" people to "strive towards the ideal and help one another" – he had no respect for Germans and their damp slave-morality, and he often seemed to regard them culturally and racially
inferior to the priestly Jews.
2) The entire Nazi ideology was a condensation of everything that Nietzsche considered base and detestable: It was reactive*, vulgar, gregarious**, slavish, and fueled by poisonous
ressentiment – a picture-perfect example of butt-hurt "slaves" (Germans) rebelling against successful "priests" (Jews).
3) Nazis did not want "other cultures and races to do the same in their own countries": There was only
one human race and
one human culture in their world – everyone else was less-than-human.
* Their entire self-concept was based on the "wrong" they had suffered at the hands of the Allies and the imaginary Jewish conspiracy.
** How could one possibly reconcile autonomous master-morality with a morality of the masses? – that's prima facie wrong.