Actually, I don't think intelligent design has anything at all to do with any interpretation of Genesis. The whole point of using the term "intelligent design" is to draw attention to the fact that ID advocates believe the evidence suggests an intelligent designer at work. Nothing more, nothing less.
Why do they call it intelligent design and not teleology?
Answer: Because teleology is a philosophical attempt at a proof for the existence of God and IDers wanted to avoid that and pretend to be scientifical.
Why did they want to appear scientifical?
Answer: Because they want it taught in school.
Why do they want to teach it in school?
Answer: Because they think that evolution alone will turn children from God.
What's the evidence that it has anything to do with creationism at all?
Answer: ID sprung into existence the moment that the courts ruled that creation science could not be taught in schools, and was marketed to the same people that creation science was. Also see: The Wedge.
So yes, ID has stripped Yahweh by name. It doesn't refer to Genesis. It is teleology in all but name, and the people that head up the movement are funded by creationist punters. The reason they call it ID is not to draw attention to the intelligent designer, but to try and avoid using the synonymous phrase 'god' and also to avoid using the already established word 'teleology'.
You see: I was taught teleology at high school as part of Religious Studies. ID doesn't want their ideas taught in RS or RE classes, they want them in the science class so they have to strip all the god stuff out, and not talk about 'creation', and replace all mentions of god with 'designer' and creation with 'design'.
They have to try and avoid people making the connection between the
teleological argument for the existence of God and the Intelligent Design argument for the existence of an Intelligent Designer.