All other primal horses, as you mention, are made from a Nightmare, but if you notice the Nightmare also has a horn, something which all primal ponies lack. I theorize part of the process of creating the primal steed has to do with the rending of the horn.

As for Shiva's steed, it is very much meant to be a different creation mythos than the rest. Shiva herself is the first time we encounter a human that plays host to the abilities of a primal, something we didn't even think possible in that part of the story. I think the fact that her steed is made from a unicorn is meant to further solidify the differences between Shiva and the other primals.

But that's just a theory. A Final Fantasy theory.