I would say that Arceus is a multi-dimensional god that has come into our universe in Pokemon form, as an incarnate deity. He* then creates all pokemon in the image of the form he* has currently chosen. The whole point of Arceus' elemental plates is that Arceus has no fixed form or powers, and although his* current incarnation is that of a Pokemon, that is not his* true form, as he* should technically be omnipresent. Of course, in this current form he* is not omnipresent nor omnipotent or omniscent, which poses a slight problem when he* is confronted by a kid with a DS, a stack of Master Balls and an Action Replay. It is therefore unfair and impossible to presume that Arceus is not a pokemon, as he* is the very definition of pokemon and created all pokemon in his form. Also, if you try to question whether or not he* is a pokemon based on his* intelligence, let us not forget that other extremely sentinent non-ledgendaries such as Lucario and Meowth do exist.
The fact is, you sort of miss the point. There is no reason why he* cannot be a pokemon and a deity at the same time. Although you claim that modern religions' gods, such as the Christian god, are not human, maybe you should think about just one word. Just one. Jesus. God in human form. This is what I believe Arceus is, a god in the form of a pokemon.
*Note: I use the masculine tense simply as a common gender, I fully regognise and accept the fact that Arceus, or indeed any of the Ledgendary pokemon, have no gender.