There is the impression, in watching Rabbi David Aaron talk about his conception of God,that he is playing with us a bit. When he says that God is not mentioned in the bible, he is fooling with the tradition.
There is a perfectly functional word for God in Hebrew, elohim, and it is used to distraction all over the place. But it is not considered the paramount name for the divinity. What Rabbi Aaron is talking about are some interpretations about the name God reveals to Moses, HaShem, the name that can't be pronounced. This is the divinity that is about non duality. There is not Him and Us; there is only a kind of oneness that transcends the human conception of oneness.
What Aaron is getting at here is that when you say the name God, all sorts of images come to mind (usually of an old man somewhere, or a being someplace that is not here). So he invites us to toss out the word, because it has too much baggage. There is a place in the Jewish tradition for a broader view of the divine: as the unfolding nature of reality, of the past, the present, the future, all at one time and in every place.
This kind of "God" gets to skip away from all kinds of troubling aspects of traditional monotheism. If this "God" concept picks up a few of its own theological conundrums, some hard nuts to crack, then it says more about the way we think, than about a non dual God.