sky writes:

"but it was not until the end of the 18th century that nationalism began to be a generally recognized sentiment molding public and private life and one of the great, if not the greatest, single determining factors of modern history. "

--

You misinterpret the definition.

Note that it doesn't say that nationalism is a new phenomenon, but that it was first recognized for what it is in the 18th century.

Nationalism has been driving wars, imperialism, jingoism nativism, tribalism etc for millennia.