I won't split hairs, but technically it is a clinometer. It is used by foresters and others to determine the height of trees and other objects by calculating the angle to the top from a known distance on the ground. The Stanley Company may use brand names like "Abney Level" but the terms "sextant" and "level" describe quite different instruments in common usage. Levels in surveying do not measure vertical angles. Sextants in navigation are designed to measure the vertical angles of astronomical objects rather than terrestrial objects and are more accurate. Tiger Exile is up.
I guess its just one of those things in the world that gets called something it isn't sometimes over the years and some folks end up naming it different. As I said my grandfather had one of these (the very same one I think) which had belonged to his brother. And I do recall something mentioned about "measuring trees" actually. Anyway, an interesting piece red.
FWIW, I wasn't trying to start anything. Your "it" was something I actually recognized right away. When you said @Tiger Exile was incorrect I questioned my own information.