I really like this thread but I am not sure if people are using the word "Primal" correctly in some of their statements. Let me at least attempt to illiterate what I mean.
In Eorzea there are many tribes which include Amalja, Ixali, Slyph, Hyur, Miqote, etc which can also be referred to as Races. These can be further broken down into 2 catergories: The civilized races (Miq/Hyur/Elezen/Lalla/Hume) and the tribal (izali/amal/slyph/gobs/quiquirn etc) races. The term Beastman is not the actual affiliation of the tribe but rather a slang word the civilized races have given them because they are less advanced and more tribal (hint there's a word that describes this perfectly....). The Amal'ja do not refer to themselves as beastmen, for instance.
It also goes to follow then, that the words Eikon and Primal are also derogatory slang terms the civilized races use to refer to the Gods that the heretic 'beastmen' tribes worship. Primal is the perfect word for this because it embodies what the civilized races feel about the beastmen, that infact they are primal themselves so that they would be summoning something of a primal nature; in other words back to the basic roots of civilization (fire, stone, wind are all PRIMAL to civilized races). [One of the definitions of Primal also means Fundamental; the elements are fundamental building blocks of the world]
In this sense, no, the Twelve are not Primal's and cannot be referred to as such. But the Primal's such as Ifrit and Garuda can be referred to as gods.
Its easier to make a chart following this pattern:
Tribe(or Race) - Kings - Gods
Example
Amal'ja - Unknown - Ifrit
Draconia - Nidhogg + Midgardsommr - Bahamut
Civilized Races - Possible the Sultana - The Twelve
Garlean - The Emporer - ??? (Odin?!)
But basically the point of my post is Primals are gods, but gods such as The Twelve are not Primals because the word primal is most likely a derogatory word given to them by those whom worship the Twelve.
I hope I explained my point well enough -.-;; Usually I'm pretty terrible at it but I think this is correct in the context of the game thus far. People from Spain that first came to the America's in the 1500's probably also referred to the natives as "Beastmen" or "Primals" when they arrived so I was thinking along the lines of something similar.