It seems unusual that Russia would be interested in supporting Ethiopia, especially to the extent they did, and with what little (apparent) interest they had in Africa.
Many countries sought to send military missions to study not only modern fighting, but also fighting in different cultures, different terrain and different climates. Sweden and Turkey also had no interests in the region after ww1, yet both sent military missions during the 20s and 30s to Ethiopia.
What was in it for Russia? Experience fighting in mountainous terrain in a hot country where the locals were a semi-feudalistic society. It is quite similar to their own recent excperience against the Circassians in the Caucasus, held value for potential fighting in the eastern parts of the Ottoman Empire, Persia and Afghanistan (all of which seemed like likely places for the next war for Imperial Russia in the 1880s).
But mostly, Russian arms companies could sell arms to Ethiopia though the Russian military mission.
The Ethiopians bought about 30 000 Berdan rifles (military surplus as the Russians were replacing them with Mosin-Nagants) and about 50 63,5mm M1883 mountain guns from the Russians.