In Aristotle, to what category does the κινητόν belong?
As this is about "movement", the motion, more precisely the outcome of it, may fall under any category, as I understand:
Again, there is no such thing as motion over and above the things. It is always with respect to substance or to quantity or to quality or to place that what changes changes. But it is impossible, as we assert, to find anything common to these which is neither 'this' nor quantum nor quale nor any of the other predicates. Hence neither will motion and change have reference to something over and above the things mentioned, for there is nothing over and above them. (Physics III.1)
Movement is to be understood as causation as such, moving the substance in different ways causing a change of accidents falling under the categories. At least this is my best shot of what is left of Aristotle in my mind. Therefore God as the unmoved mover must be thought as the beginning of every single causal chain of events, bringing the substance of things into motion:
Moreover, the conclusion to which we have been led is a reasonable one. For there must be three things-the moved, the movent, and the instrument of motion. Now the moved must be in motion, but it need not move anything else: the instrument of motion must both move something else and be itself in motion (for it changes together with the moved, with which it is in contact and continuous, as is clear in the case of things that move other things locally, in which case the two things must up to a certain point be in contact): and the movent-that is to say, that which causes motion in such a manner that it is not merely the instrument of motion-must be unmoved. Now we have visual experience of the last term in this series, namely that which has the capacity of being in motion, but does not contain a motive principle, and also of that which is in motion but is moved by itself and not by anything else: it is reasonable, therefore, not to say necessary, to suppose the existence of the third term also, that which causes motion but is itself unmoved. So, too, Anaxagoras is right when he says that Mind is impassive and unmixed, since he makes it the principle of motion: for it could cause motion in this sense only by being itself unmoved, and have supreme control only by being unmixed. (Physics VIII.5)
This is very similar to what Kant writes in the thesis in the third antinomy in the Critique of Pure Reason about transcendental freedom, by the way.
Movability in this narrow sense (kineaton) could be then attributed to anything but the free, but generally only to substances.