It's really just a diatonic Gm thing as far as I'm hearing. If you just vamp between an open D and G string you can sort of hear pretty easily where it's revolving around, and wank a G nat. minor over the top and you won't get any bad notes.
Chronowarp is right. The first two are G natural minor and the 3rd is F minor.
What makes it distinctive is - in all 3 of them - there's a lot of focus on the b6 of the scale, often holding it over the chord. Eg, in the first one, he often plays an Eb triad over the G bass groove.
In the 2nd one, the horn phrase ends on a long Eb, again over the G bass. (Eb is the main note, harmonised I think with Bb and G to make the triad.)
It's that b6 (against the P5) that gives it a phrygian vibe, but there is no b2. In the G minor ones, there's clearly an A in the scale (not Ab), making it aeolian.
A lot of EthioJazz is based on local pentatonic scales. Lookup Tezeta (a local notion close to the feeling of "the blues", or "saudade", etc.), lookup the Krar (a traditional five (pentatonic) string instrument), find out about the Ethiopiques record collection, the effort that pretty much resurrected this wonderful music.
For the song you've posted about (Yegelle Tezeta, Yekermo Sew), use G A Bb D Eb. You have 1 2 b3 5 b6. 4 is pretty much an avoid note but you can mess around with b5 and both 7th too.
As Sir JonR said, a lot of those grooves in Gm are based on Gm and Eb triads, so mix and match with this pentatonic scale and focus on the phrasing of those guys, or else you'll loose that distinctive and magic ethiopian flavour. Give an ear to singers like Mahmoud Ahmed too, some gems are hiding there.
For Yekermo Sew he is using an Ethiopian scale called the "Half Tizita". It is a pentatonic minor scale. The note intervals are a major 2nd, minor 2nd, major 3rd, minor 2nd, and a major 3rd (1, 2, b3, 4, b5). In G minor this works out to be G, A, Bb, D, Eb. So basically a G minor without the C and F notes being played.