https://musescore.com/user/1108766/scores/9410239
(BTW, there are several versions of this song on the Current 93 album _Black Ships Ate the Sky_, of which my favorite is Shirley Collins'.)
So my guess is that if shape note singers call it "treble" it's because historically it started as a male-only thing, with sopranos (women) and female altos joining later while keeping the tradition of calling the top part "treble".
The alto part seems to be a different story though. In fact, in one of the old shape note tune books I've got (a reprint of The Southern Harmony, originally from 1854), the alto part is labeled "counter", suggesting it was adapted from the Reformation-era countertenor parts. It was occasionally sung by boys, or by women, but often left out entirely (most of the tunes in the Southern Harmony are three part, with no alto). Later on, this "second part from the top" reemerged as a standard alto part, labeled as such, and sung by only women and possibly boys (but by this time, certainly not men in falsetto).