They only propose that according to their theory logic demands a single uncaused cause for all and that various phenomena support the theory of design better than randomness and therefore the implication is intelligence.
That places the ID discussion on the very edge of science, where it becomes metaphysics in the sense of the word which Kant meant - what comes after physics. As such, it is a proper object of science, although hardly the kind of science you should be teaching in school rooms.
But the identity of this intelligence is beyond the scope of their theory just as it is beyond the scope of the theories of most astrophysicists who restrict their analyses to that of existence at its earliest moment and no further back.
And so it isn’t theology either. Now that is something we can get our teeth into. Thanks, Mark, for the interesting post.