I remember seeing this video a few years back. It is quite beautiful, though not a historically accurate arrangment of the melody (which is the part I assume is 800 years old). There's too many 3rds. early christian chant didn't like thirds much - and never on strong beats like a cadence. It also wasn't really "major or minor", but modal.
for perspective, this is what these melodies sound like
Another fun fact, the Icelandic Parliament, the Althing was founded hundreds of years before this chant was written, in 930 - It's the world's oldest parliament. I've been to Thingvellir, which is the site that the Althing used to be held at. The land there is literally on a tiny plate between the North American and Eurasian plates, and you can see the continents pulling apart.
another tertiary fact - Thing, in older germanic languages, held a meaning of "gathering", so Althing is "gathering of all", and thingvellir is "gathering valley"