I suspect Apple are trying to protect themselves from expensive warranty claims. I expect the nano-coating is VERY expensive for them to replace (most likely having to completely replace the entire screen) and by stipulating specifically a cloth with a known fiber count and nap they know can't harm the display and then specifying you HAVE to use it they can eliminate claims by people using cheap scratchy 20c microfiber cloths or office screen cleaning wipes thus saving themselves the hassle and expense by giving them an "out" on repairs, plus it's a extra revenue stream from people and companies for whom the cost of a replacement cloth is utterly insignificant.
There's probably nothing special about the cloth (above other expensive microfiber cloths), except that it's of a known quality that Apple knows is safe.