That's because Artsakh (Nagorno-Karabakh) is internationally recognized as being part of Azerbaijan. Even Armenia itself does not officially recognize the independence of Artsakh. Thus from a Russian point of view, Azerbaijani military attacks on Artsakh are an internal matter for the Azerbaijan government and not an act of aggression against Armenia proper which would trigger their mutual defense treaty.

During the war, both Armenian and Azerbaijani forces were doing a kind of kabuki dance, provoking the other side into bombarding either Armenia or Iran, to trigger either regional powers' intervention in the conflict.

It's a sad reality for the Armenian people that they were never truly independent and sovereign, but always a protectorate of the Iranians, Romans, Byzantines, Turks or Russians. I think everyone in Western leadership circles (or at least those who can actually place Armenia on a map) recognizes that and there is not the antagonism against them that, say, Belarus or to a lesser extent Serbia is experiencing.