Mike, do you know anything about the shape note tradition? If you don't, you will some fascinating stuff to explore.

I listened to your link, and the sound of people singing the syllables of the scale (la, so, fa, do, etc) told me that this is a shape note song. Then I googled this:

shape note "King of Peace"

and found lots of info on the song you are interested in.
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If you are versed in shape notes, then 'King of Peace' is a hymn from the the Sacred Harp. When John Jacob Niles was collecting music in Kentucky and saw that a family had a copy of the Sacred Harp, he'd get all excited. He knew they were likely to like and share old music.

I"m thinking of adding King of Peace to my own repertoire.