Okay, here's the Zombie World argument, paraphrased:

1. It is "conceivable" (whatever that means) for there to be a universe with physical laws exactly identical to ours, but without the "bridging psychophysical laws" that cause certain physical configurations of atoms to produce subjective awareness, i.e. "consciousness".
2. By assumption, the universe described above is physically identical to ours, right down to the last quark. As a result, there is a planet called "Earth" in this universe, and this planet is populated by humans identical to ourselves; each of us has a counterpart in this other universe. Moreover, each of those counterparts behaves exactly like you or I would, talking to each other, laughing at jokes, and even falling in love.
3. However, since this hypothetical "conceivable" universe lacks the "bridging psychophysical laws" that are necessary for true consciousness to exist, each of those people in that universe, despite acting exactly like you'd expect a conscious being to act, aren't actually conscious, i.e. they don't experience qualia or possess any sense of self-awareness at all. They are, for all intents and purposes, automatons.
4. Since by definition, there is no physical experiment you can perform to distinguish our universe from the Zombie Universe, any observer would have be told, as a separate and independent fact, that "yes, this universe is not the Zombie World--there is actually consciousness in this universe". This is then taken as proof that consciousness must be extra-physical, i.e. epiphenomenal.
5. In both the Zombie World and our universe, people write philosophy papers about consciousness, since (again) the Zombie World and our universe are stipulated to be physically identical, and the act of writing a philosophy paper is a physical act. Incidentally, by the way, this means that the philosophers in the Zombie World are being absolutely crazy, since they're talking about a phenomenon that they have no way of knowing exists, by definition.
6. However, it turns out that our universe's philosophers (whose beliefs about consciousness are no more justified than the Zombie World's philosopher's beliefs) actually are correct about consciousness, because by sheer miraculous coincidence, they happen to be living in a universe with the correct "psychophysical laws" that produce consciousness. They are correct, not because of any logical reasoning on their part (indeed, the reasoning they used must be flawed, since they somehow deduced the existence of a phenomenon they literally have no way of knowing about), but because they just happen to be living in a universe where their statements are true. Yay for them (and us)!
7. Oh, and by the way, we really are living in a universe with consciousness, not the Zombie World. I know that there's literally no way for me to prove this to you (in fact, there's no way for me to know this myself), but just trust me on this one.

And now here's my argument, paraphrased:

1. It is "conceivable" (whatever that means) for there to be a universe with physical laws exactly identical to ours, but whose "bridging psychophysical laws" are such that only those physical configurations of atoms corresponding to my (dxu's) brainstates produce consciousness; nothing else is or can ever be conscious.
2. By assumption, the universe described above is physically identical to ours, right down to the last quark. As a result, there is a planet called "Earth" in this universe, and this planet is populated by humans identical to ourselves; each of us has a counterpart in this other universe. Moreover, each of those counterparts behaves exactly like you or I would, talking to each other, laughing at jokes, and even falling in love. One of those people is a counterpart to me; we'll call him "dxu-2".
3. However, since this hypothetical "conceivable" universe has a different set of "bridging psychophysical laws", each of those people in that universe (with one exception), despite acting exactly like you'd expect a conscious being to act, aren't actually conscious, i.e. they don't experience qualia or possess any sense of self-awareness at all. They are, for all intents and purposes, automatons. Of course, I said there was one exception, and that exception should be obvious: dxu-2 is the only person in this universe who possess consciousness.
4. Since by definition, there is no physical experiment you can perform to distinguish our universe from the Modified Zombie Universe, any observer would have be told, as a separate and independent fact, that "yes, this universe is not the Modified Zombie World--everyone here is conscious, not just dxu-2". This is then taken as proof that consciousness must be extra-physical, i.e. epiphenomenal.
5. In both the Modified Zombie World and our universe, people write philosophy papers about consciousness, since (again) the Modified Zombie World and our universe are stipulated to be physically identical, and the act of writing a philosophy paper is a physical act. Incidentally, by the way, this means that the philosophers in the Modified Zombie World are being absolutely crazy, since they're talking about a phenomenon that they have no way of knowing exists, by definition.
6. Dxu-2, by the way, isn't a professional philosopher, but he's fond of making comments on the Internet that assert he's conscious and that no one else is. Of course, when he makes these comments, his physical self is being exactly as crazy as the other philosophers in the Modified Zombie World, but luckily for dxu-2, the drivel that his physical self types just happens to be exactly right, because by sheer miraculous coincidence, he lives in a universe with the correct "psychophysical laws" that cause him to be conscous.
7. Oh, and by the way, the Modified Zombie World is our universe, and "dxu-2" is actually me. I know I can't prove this to you, but just trust me on this one.

If you accept the Zombie World argument, you have to accept my argument; the two are exactly analogous. Of course, the contrapositive of the above statement is also true: if you reject my argument, you must reject the Zombie World argument. In effect, my argument is a reductio ad absurdum of the Zombie World argument; it shows that given the right motivation, you can twist the Zombie World argument to include/exclude anything you want as conscious. Just say [insert-universe-here] is "conceivable" (whatever that means), and the rest of the logic plays out identically.

P. S. One last thing--this part of your comment here?

No [one] thinks that the real world is a zombie world.

If the Zombie World exists (which I don't believe it does--but if it did), all of the people in that universe (who don't think their world is a zombie world) are dead wrong.