What he says is actually surprisingly irrelevant- have you ever heard the phrase 'the author is dead'? In the books it is clear that the Red God and the Old Gods have power. It would take quite a leap of logic to insist that they don't exist- particularly the Red God, whose power has been shown to the reader so many times. The other Gods might not exist at all, however. I don't believe we've seen any of their followers display any form of supernatural abilities (except, I suppose, the God of Many-Faces).
Not really, it could be just as firmly argued that the weirwoods and the red priests have magic. The books tell the world from the perspective of the characters who only know what they see and are told. Maybe the Gods have Power, But its just that in this setting Magic is a force of nature that effects many things and the people believe its Gods and not Magic.
You might as well site the greeks legends that give Gods as the source of tides or winds as evidence of the existance of Greek Gods in our world. The Greek protagonist thinks the wind comes from a cave, so the narrative, from his perspective says it does, but that doesnt mean it does, just that the characters in the story think it does.
Melisande might be a witch, who believes that her magic isnt magic but really miracles. Or she could just be a woman that the Red God is working through, or some secret child of the forest or ghost or some other magical creature might be working through her for that matter and playing on her beliefs to get away with it.
We dont know the truth of it, we just know what she thinks the truth is and what those around her think is true. But the perspective based narrative
doesn't give empirical facts, just opinions.
Theres too much suggestion to either side to say anything definitive, for example its heavily implied that the Red God comes from misinterpreted folk memory of a hero of an earlier age and yet the Red Priest can break the natural rules and make miracles or spells.
While itd take a blind leap to say that dont exist, its an equally blind leap to say they do. The Setting never puts it definitively either way.
It's not important to the story if the Gods of that world exist or not, so the books have never gone into it.
Either way, the gods in the books if they exist or not, would that effect the politics of the westerosi nobility?
And if not then theres no reason to represent them in the game. The World has fish in, but the game doesnt bother to represent fish as they have no impact of anything represented by the game.
So it doesnt matter.