I'm not convinced that's true. (It's typically part of how they imagine their "God", but nowhere close to exhausting the concept.) But even if it was definitive of the word 'God', how would that be relevant?
Of course it doesn't exhaust the concept, nobody suggested that it does.
It is relevant inasmuch as this is their definition of "God," and if anyone is going to engage in discussion with IDers, it's important to clarify the meanings of the terms used.
"Intelligent design" arguments don't begin with some theological definition of "God", and then proceed downward from there. Instead, they begin with what they claim are thoroughly scientific principles and observations in this world, and then argue that these lead upwards to the conclusion that some God-like being exists (somewhere).
Clearly the "ID" proponents are crafting their arguments so as to lead to their desired theological conclusions. But brazenly introducing those desired conclusions among their argument's initial premises would render the whole thing circular.
So what "ID" does is start with some this-worldly and ostensibly scientific observations that (they argue) can only be interpreted as evidence of intelligent design. It's rarely clear what kind of observed data is supposed to be evidence of design, unfortunately. I've suggested in earlier posts that what "ID" proponents often point to are examples of functional form, structures that can be said to perform functions and that lend themselves to functional explanations. We often encounter functional explanations in biology.
The same kind of objections can be launched against ordinary science.
Both IDers as well as scientists look at the world, and then make claims about its essence. Sure, they make different claims, but both have in common that they make claims about the world's essence simply on the grounds of looking at the world (and refuse to acknowledge their own projections).
The problem is that if forms that perform functions must (for some reason that isn't entirely clear) point beyond themselves towards a different intelligent designer, then consistency and the logic of the whole argument would seem to demand that the hypothetical designer would need its own designer, and so on... in an infinite regress.
Just like IDers operate out of axioms (one of them being that God is the First Cause), so ordinary science operates out of axioms.
Referring back to one's axioms is not the fallacy of special pleading. It is simply not possible to have any kind of discourse without first positing some axioms.
Obviously this isn't consistent with traditional theistic theological doctrines. You are right about that. The thing is, that shouldn't matter, unless those theological doctrines are really the starting point of the whole argument. They probably are in real life. But the "ID" argument is purporting to be something very different than religious special-pleading. It's purporting to be an entirely scientific and non-theological line of argument that (so its proponents insist) leads inexorably to something very much like their own desired theological conclusions.
Same principle is at work in with science. Scientists are very much invested into a materialistic understanding of life, and their theories are geared toward "proving" that matter is all there is.
But if we adopt somebody's theological definition of what the word "God" supposedly means as one of the "ID" arguments' initial premises, then the whole "ID" argument is rendered circular.
You wish to talk about "God" and make claims and extrapolations about "God" - without first defining the term "God"?
It also seemingly becomes inconsistent with the argument's supposed observational premise that instances of functional form (or whatever it is) point to something other than themselves, something that supposedly designed them. Once we have that (supposed) principle installed and up-and-running, the new problem appears of justifying why the design => designer principle should be shut-off again just because somebody's desired theological conclusions have been reached. If it isn't shut off, we have an infinite regress.
Again, the same with science: Why shouldn't we question science's axioms? Why must we keep our inquiries in line with science - but only up to a certain point, from which on there be dracones and we must shut off all inquiry?
The way I see it, the weakness of ID criticism is that the critics accuse the IDers of exactly the same things they themselves are guilty of. Which is how the whole thing remains so upsetting, never getting resolved.
It is my estimation so far that the ID movement in the US, along with the citicism of it, is taking place in ways that would not be possible in, say, Europe.
The general atmosphere in the US seems to be one of supposed free speech, First Amendment, personal freedom and "pursuit of happiness" (you have that in the Constitution), a spirit of entrepreneurship and competition, but also accompanied by a tendency toward litigiousness.
Given this context, I don't make too much of the actual arguments used in the ID debate by either side. I see no hope of settling the matter philosophically (or scientifically) as long as the social context is what it is.
It seems that per US standards, for either side to prevail, the civil rights of the other side would have to be trampled.