There are a substantial amount of Azerbaijanis in NK as well. To me it seems like Armenia wants it because of its historical and cultural signifigance (especially as it pertains to the Church) while the Azerbaijanis want it more to access Iran and the broader Caucasus region.
Perhaps Russia's goal is to politically, economically, and diplomatically align the Caucasus, and they see peace in NK as the means of getting there.
It makes sense too because both Armenia and Azerbaijan exist at a geographic periphery, with not many influencing forces. Russian guidance almost seems to be expected.
For the West, I think we have admitted many times over that the region just isn't of much concern to us (NK at least).