bear in mind that they were also busy fighting amongst themselves for some 500 or more years, trying to figure out who was in control of what, long before there was ever a concept of "China."
Rome and Persia succeeded so well b/c there was a single power structure. Once we know who is in charge, let's go out and start conquering. Much in the way that there was no concept of unification amongst the modern Italian states any time before or after the Roman empire (bear in mind that "Italy" was not a name that appeared in the history books before the late 19th century--technically speaking, the USA is an older country).
Ancient China had the military might that would have been more than capable of taking what they wanted, were it not for the extreme hubris amongst the tribes, or clans, or families, whatever you want to call them. Fortunately, this kept them out of the game for so long. Had the current mentality of the Han Chinese of today existed at that time, under a hypothetical unified continent (We own everything, just because, so fuck all youse!-ergo Taiwan, Tibet, etc.), the world would be a very different place.