Well, unless with dualism you just mean that there are two, you are simply mistaken. Just because my car has an inside and an outside, and I cannot determine the state of its gearbox from the outside w/o the car telling me, does not mean that this implies a ghost in the machine. Far from it.
He makes the analogy that a weather simulation in a computer can't make anything wet so therefore a computer program can't have a thought. My take is that when we think about rain we don't get wet either. Human minds are the same sort of thing as the weather simulation, not the same sort of thing as the weather. For me thoughts are simulations, or models, or operations on models, and that those activities are tractable to computation.
Doesn't that beg the question?