Your correct with the analysis but it's actually down to the difference between the imperfect nature of the physical world and the timeless nature of the world of ideas. It's a god as much as a god can be in the physical world which by definition is imperfect. This has a lot to do with Plato's world of shapes/forms.
In our world there is no such thing as perfect, we have the idea of something being perfect but that can't exist in the real world. Even when it comes to zodiark he isn't perfect. When the idea is manifest it is brought forth using the understanding of the caster whose understanding of the concept has been influenced by their culture, religion etc as well as their natural talents and available resources but the fundamental nature of the concept hasn't changed and you can argue that the fundamental nature of concept itself directed them to perform the summoning which in turn would promote the concept. Aka do people have ideas or concepts or do concepts and ideas have people who use them to manifest the concept and spread its influence further?
The difference between the ancient method and what was later taught is that the concepts which manifested were stable concepts they didn't require constant sustenance. The concept of a god didn't really exist for the ancients because they themselves had no need for one in the traditional sense until they did which was to manifest the concept of salvation. You could also argue that concepts did eventually become more than sums of their parts because almost every enemy type we see in the game was a stable concept created by an ancient in Elpis with their own emotions, feelings etc.
It also comes down to how we define a deity or a true deity. Do we compare them to the incredibly human and imperfect pagan gods which fed on faith, sacrifice and ambrosia or do we compare them to the Godhead of the Abrahamic religions where God is the beginning and end, we they are all-powerful. All-knowing and ever-present. If that was the case the only person in the setting who could be considered a god would be Athena when she tried to transcend into an all-powerful being who tried to recreate reality.
The simple truth is a God is a being which is worshipped due to it being connected to ideals that people see as transcendent and universal such as justice, nature, war, love, desire, chaos, death etc. Also, almost anything can be used as an idol, to worship said God a good example in the Bible would be the Golden calf which was an eikon of the Egyptian bull god Apis.
Plato's theory of forms
“ These Forms are the essences of various objects: they are that without which a thing would not be the kind of thing it is. For example, there are countless tables in the world but the Form of tableness is at the core; it is the essence of all of them. Plato's Socrates held that the world of Forms is transcendent to our own world (the world of substances) and also is the essential basis of reality. Super-ordinate to matter, Forms are the most pure of all things. Furthermore, he believed that true knowledge/intelligence is the ability to grasp the world of Forms 's theory of forms”
Also on perfection of ideas
No one has ever seen a perfect circle, nor a perfectly straight line, yet everyone knows what a circle and a straight line are. Plato uses the tool-makers blueprint as evidence that Forms are real
... when a man has discovered the instrument which is naturally adapted to each work, he must express this natural form, and not others which he fancies, in the material ....
Perceived circles or lines are not exactly circular or straight, and true circles and lines could never be detected since by definition they are sets of infinitely small points. But if the perfect ones were not real, how could they direct the manufacturer?