Likewise, the definition doesn't give any hint what "intellegence" is. Nor does is give any indication that such a determination is possible.
That is correct, but as stated above, a definition of intelligence is not necessary to classify a hypothesis as an "intelligent design" hypothesis. All that you need is that the cause specified by the given hypothesis be intelligent.
The objection you raise, also raised in a different context by xzins and PatrickHenry, derives so far as I can tell from the fallacy of the excluded middle that is so common amongst ID theorists such as Alamo-Girl. It appears in statements such as this (fabricated by me as an exemplar):
The eye is irreducibly complex, therefore since the odds of an eye springing fully formed out of the ether are infinitesimal, some vague, undefined intelligent actor created eyes.
When you try to pin down the intelligent actor, the answer given by ID advocates is something along these lines (again fabricated by me as an exemplar):
Umm.. It could be god, random particles floating around interstellar space, or, you know, something kinda like the groupthink.
Since they don't bother to specify the intelligent designer (a question that we have pending), then you have this question of: What is "intelligent" and what is "intelligence" for the purpose at hand.
But, in any event, I have had every intention of addressing the point whenever we get to the stage of classifying "panspermia" and "collective consciousness" (which we're not doing yet). We cannot classify anything as an intelligent cause unless we establish that it is in fact intelligent..