Remember this page of Norwegian folks songs? #10 on that page is our song. Click through to find two different tunes given. The first tune is the one used by Trio Medieval and Glitterind. The second tune is the first one given in that Danish 1908 book of Faroese tunes; there are four tunes total given.
They are similar but not the same. Most notably, in the second and fourth lines, the more modern contour proceeds through scale degrees 5-3-4-1-3-2-7-1. The dance tune proceeds 5-3-4-3-1-3. (EDIT: Scale degrees are for Dorian mode. Add 1 to all the numbers to get the scale degree for the major scale.)
The "2-7-1" cadence is a major folkie thing, IMO. The Faroese dance does give an alternate tone on degree 2 for the very final cadence; it gives 3-5-1, with a smaller note on 2 written under the 5. Harmony on a fourth? A variant? I'm not sure. And some of the other tunes at least do use scale degree 1, although not that I noticed in that particular telling pattern.
I'm not surprised that I had a hard time telling that the tunes were in fact different at first look. But now I know why the video of the Faroese dancers didn't quite sound like the other performances.
I'll have to give a more careful listen to some of the Faroese tunes. It's sort of a philosophical question - all the tunes under consideration are only documentable to the 20th century, but the Glitterind tune with that cadence sounds even more 20th cen to my ears. But it also sounds good.
Tablature for comparing the two tunes under the cut.