The epiphenomenalist imagines eliminating an effectless phenomenon, and that separately, a distinct phenomenon makes Chalmers go on writing philosophy papers. A substance dualist, or reductionist, imagines eliminating the very phenomenon that causes Chalmers to write philosophy papers.
Right, so that's a bad way to present the argument. The better way to imagine the zombie world is not by subtraction, but by building it up. Give a complete microphysical description of the world, and specify "that's all". A Laplacean demon can infer that the world contains tables, brain states, and a book entitled 'The Conscious Mind'. That is, the world contains particles arranged table-wise, brain-wise, book-wise, etc.
The Laplacean demon knows all that there is to know about this world. Does he know that it contains phenomenal consciousness, that there is something it is like to be the particles-arranged-humanwise in this world? Seems not. There's nothing in the microphysics that entails the presence of such subjectivity. So we've successfully imagined the zombie world. Not by subtracting, but by building up from the physics alone and noting that more needs to be added in order to obtain our (consciousness-containing) world.
Richard Brown makes a similar mistake in his attempted parody:
I am conceiving of a world that is just like this one in all non-physical respects except that it lacks consciousness. Therefore dualism is false.
The zombie argument begins by providing an undisputed specification of the "physical respects" of the world. It then asks whether phenomenal consciousness logically follows from the specification. Our answer is 'no'. That's why physicalism is false.
A proper analogy, then, would require building up the "non-physical zombie" world from an undisputed non-physical specification, just as we earlier built up a physical zombie world from an undisputed physical specification. But of course RB cannot do this. So that's why the zombie argument cannot be turned against dualism in this way.