As much as Hildy's story is comedic, the one where Enkidu actually came back was also one of, if not during THE most serious part of the whole quest line. As well, Gilgamesh himself has been used as a summon in multiple games, yet he for sure isn't an Esper, Guardian Force, or anything like that...now whether this means Gilgamesh can summon in a different way BECAUSE he isn't from Eorzea, or if it just means he has an easier time summoning on his own but Enkidu was still a primal is something related but different.