The term ‘noble savage’ was originally the product of quite a simple observation: that the tribal peoples of North America tended to spend their time on the same sorts of activities that occupied European noblemen: hunting and warfare. On games.
The term only later came to refer to their spirit of goodwill, and romantic ideas of their perfect harmony with nature and each other.
The savages were not acting like nobles; the nobles, free of material constraint, were bound to occupy themselves in accordance with the deep yearnings of their genetic code, and do their best to live like human beings. This is what Nietzsche saw–the nobles get to be alive, and affirm life. Because they alone get to LARP being hunter-gatherers. Naturally, a class of people, given infinite resources and left to their own devices, would eventually gravitate towards that for which their every cell is honed.
But in the Americas were found a whole race of people living this way, people for whom God was not dead but was life itself, the rhythmic dance, the ocean which held them in its embrace no less than the lilies and birds.
And unlike the nobles whose bodies were sustained by a much larger class of shit-shovelers, and whose games produced nothing of value, these savages sustained themselves through their play. Their relation with the world was a thing of joy. They were fed through their play. The business of living, of material sustenance, and the business of enjoyment and delight, were one and the same.
Hence, Noble Savages.