I think one of the reasons why Humes appear to be the dominant is mentioned in the Strategy guide and I think the Ultimania which states that the Humes are the most social and pioneering of the races. They are quite widespread and its a possibility that the other races either take advantage of the Humes handiwork (Seeq and Viera) while others see benefits for trade and cooperation (Bangaa and Moogles).

Its hard to judge how the racial structure works in XII since we are only taking part of a small part of the world of Ivalice but I'm pretty inclined to go with Big D on this. The Humes look down on the other races in some form another. Hell, I remember a moogle in the bar at Bhujerba yells at you when you talk to him cause he goes on about how stupid Humes are and how silly it is not to think moogles enjoy alcohol as well. I know the Seeq and Bangaa complain about racism from the Empire in Nalbina. The Nu Muo seem restricted to Mt. Burimasce so we get little info on them. All the races seem to look down on the Seeq.