What do you think the anamorphic camera lenses you mention do? They squish a wider aspect ratio image onto a narrower aspect ratio film.
Film has nothing to do with how an anamorphic lens works. The lens simply bends the light - a completely optical process.
Referring to such reshapeing methods ussed with DVDs is not neologistic.
It is, because the original (AFAIK) meaning of anamorphosis has to do with optical tricks, and the methods used on DVD players have nothing to do with optics. By the time optics are even involved in the process (the picture going from the monitor to your eyes), the "unsquishing" is already finished.
As for etymology, the Latin prefix "ana-" has a few meanings, and the one relevant to the term in question is not "up" but rather "again".
The one relevant to the term as we're using it is "up."
as there is no reshaping of the content when adding letterboxing for a narrower display, just like there is no reshaping of the content when adding pillarboxing on a wider one;
If you really want to disregard all meanings of "ana" other than the one that works best to describe anamorphic lenses, it can work here too. When you add black bars on top of and below a rectangle, you are in a sense "reshaping" a wide rectangle into a less wide rectangle. But I like my "up" explanation better.
Another point worth noting is that the term has been used to describe 1080p video content, even though 1080p uses square pixels and doesn't involve any squishing. The term has simply come to mean "fixed aspect ratio with black bars on the top and bottom to make up the width difference."