It's not really a theme in XIV, it's somewhat of an exception on how the primals work. They are basically summoned out of strong feelings, generally by several people but in some rare cases by a single person and they are given form based on collective subconscious. Shiva isn't tied to a single person either, nor are some of the later primals that are summoned by taking possession of a body, it's just a way to channel the aether and give it form more easily and without requiring as many crystals.
The XVI take isn't really the same. Granted, it's not an original take either, it's an overdone anime trope, people having some hidden entity living within them giving them huge powers and being used for war. Hell you don't even have to go for obscure anime here, this is the basic of Naruto's story. You just replace the tailed beasts by FF summons and ninjas by knights.
I wouldn't really extrapolate too much about the story based on this limited trailer though. Chris was bitching it wasn't "FF enough" but the big twists are never revealed in the trailers especially the very first trailer. For all we know this is the first 5mins of a game then you get hit by a truck, meet God and are sent to a VRMMO world where you begin your adventure to become the best mailman in town.