You can't tell if this song's home mode is G dorian or A phrygian. It's both. The riff at the beginning starts on G like G is the root and ends on A like A is the root.
If I'm counting it right, the riff is played over a changing meter of 3+2+3+4+4. The first diversion in the opening instrumental part (0:18) switches to a steady meter of four and, interestingly, the mode switches to G aeolian at the same time which, like the regular four beat meter, is more "normal" to us. The chord progression is:
G minor/Bb major/C minor/F major
This phrase ends, however, by going back the G minor to A minor chord progression, so we're back in the original modal territory. It stays there for another phrase, but then there's a change.
At the downbeat at 0:38, there's a D minor chord. I'm going to say it's a root chord and we've switched tonic notes. The chord progression you hear is:
D minor/G major/D minor/G major/F major
So, it's a tonic note but it's a modal tonic note. The phrase is in D dorian.
When the singing starts, there's a repeat of some of the musical materials, but a new segment is also heard at 1:19. At the downbeat here, there's a C minor chord. I'm going to say that this is a root chord, too. We then follow a few diatonic chords in this manner:
C minor/Eb major/Ab major/Bb major
Two more amazing things happen before the passage ends. One is a gorgeous reiteration of the opening chords (back in the home mode), yet this time staying within the four-four beat pattern. G minor, D minor, and A minor.
The verse ends, however, with G major and F major chords, a little allusion back to that D dorian passage heard earlier.