There's a book that came out some years ago,
Proust and the Squid, by Maryanne Wolf, on the subject of reading and the brain. Part of the book discusses dyslexia. Now, I read it years ago, the book is fairly dense at times, and neuroscience is not my field. With those disclaimers in mind, let me offer a guess.
Paraphrasing wildly, Wolf said that writing as a technology is something we built by repurposing different areas of our brain that evolved in response to our pre-literate environment. Our brains didn't evolve to read. Reading is one of those marvelous things that we hairless apes have managed by pushing ourselves. It's what we do.
Dyslexia is, essentially, to put it in computer terms, the result of slow throughput in the cognitive system we've built from our (spoken) language part of the brain and our visual-spatial part (which probably evolved in response to recognizing details on the landscape, etc). In most people, when they learn to read, the brain "wires up" this system in an efficient way. It's wired up cleanly. In people with dyslexia, the wiring is more like a rat's nest — or maybe "spaghetti" would be a better way of putting it. (Again, I'm paraphrasing!)
Dyslexia is more prevalent among left-handed people. It seems like (if I remember left and right sides of the brain correctly), language is on one side of the brain, and visual-spatial is on the other. Now, left-handed people are right-brain dominant. And, if I remember correctly, left-brain dominant people are better at wiring up their brains, when the "wiring" needs to cross over from one side of the brain to the other. In general, right-handed people do a better job at building a "system" than left-handed.
Regarding Chinese and Japanese, the article talked about the way these writing systems are taught: namely, students are made to sound out what they're writing, over and over. So, if I were to guess, this slow and deliberate practice recruits all the parts of the brain involved more energetically, and as a result helps the individual compensate for any innate, relative deficiency in building a cognitive system that coordinates left and right sides of the brain: meaning, wiring up a brain that can read.
That's my best guess. Speaking out loud while learning to write may be the critical difference.