I know, and actually that's how I assumed/read it.

I think we both agree that nondenominational deities are not religious material (by definition). They have a certain appeal because they don't immediately contradict observation, but they're currently just as impossible to prove as, say, any of the Christian god variants. I'd argue it's a mistake to postulate non-religious gods but allow religious claims to take shelter in them, on account of some perceived common property.

It's true that making a "god" more generic increases the likelihood of existence, on a statistical level. But our scientific models do fine without any supernatural consideration at all right now. I would argue to keep it that way until we actually see supernatural agency at work. Until then there is not really a reason or need for it.