If you take each group of people in the New World to be an item, then the title is essentially saying "why didn't the various different groups of people in the New World invent the wheel" - it's trying to emphasize that each of group of people is actually being considered a singular entity. Whether or not this is actually grammatically correct, I don't know, though intuitively it seems quite reasonable to me (which is generally a good first approximation of grammatical accuracy for native speakers).

It's correct.

"Why did the various people..." is shorter than your comment.

One people, several peoples.

"People" is not only the plural of person... it carries several meanings, in this context : "The entire body of persons who constitute a community, tribe, nation, or other group by virtue of a common culture, history, religion, or the like: the people of Australia; the Jewish people."

From http://dictionary.reference.com/browse/people

Ignorant grammatical objections like this are just pure pollution in comment sections and warrant a full removal of the whole thread, including my comment.