All right, to spell it out: Merriam-Webster is not a dictionary of "correct" forms. The usage of "literally" in my post is documented in Merriam-Webster as "used in an exaggerated way to emphasize a statement or description that is not literally true or possible." It would be inappropriate to use "literally" in that way in a science article in the New York Times, because the standards for writing in the New York Times are different from the standards for inclusion in the Merriam-Webster dictionary.
Oh come now. You can't expect writers and editors for a company like The New York Times to know and use proper spelling and grammar, can you?
Seriously though. So annoying.
How dare they use an accepted form from Merriam Webster. (Personally I use millennia but if millenniums is accepted use in MW, that puts it well into the range of standard US usage.)