Chinese discovery of America in the first half of the 15th century opens up many possibilities for you to play with by the time the game begins. There would be long decades of Chinese influence on North and Central America before the Europeans show up. First and foremost, the native population would be exposed to Old World diseases carried by the Chinese, and by the time the Europeans arrive - their population would have probably recovered, and now with some immunity to these diseases, so no mass plagues paving the way to conquest as was in the real world. Or far smaller plagues involved. Also, by the early 1500s, the Central American native powers will probably have some contact with the Chinese West Coast colonies. Even with indirect trade, this could mean Montezuma II facing Cortez with Chinese guns! Possibly horses, too.
So European conquest would be far more partial than in the real world. The Central American native powers will possibly be players in the Great Game of the Carribean - possibly with ships made to Chinese specifications - and possibly be Chinese client-states. This creates the equivalent of the OTU Sword-Worlders and Vargr...
This makes everything very interesting indeed.
I hadn´t thought quite that far. But you´re right, it changes quite a bit.
Zheng He´s voyage to the Americas would have taken place in the 1420s, so it is very unlikely the Chinese presence in the Americas (center far to the North in Northern California) would have been strong enough to affect the civil war that led to the formation of Aztec Empire. I´m not sure the Chinese would be as vigorously and imperialistically expansionist in the America as the Spanish were; "Xinjiang" ("New Territory") is a lot further from China than New Spain is from Spain, and the Ming (like many Chinese dynasties) were more interested in receiving tribute than outright ruling barbarians, and 15th century Mexico was densely populated and quite civilized rather than (to Ming sensibilities) savages-filled wilderness like the American Southwest (which would have reminded them far too much of Mongolia for their taste) and thus far more able to resist conquest.
I think, then, that the "status quo" when the Spanish arrive is a coexistence between Aztec Empire and Xinjiang Chinese, alternating between peaceful coexistence when an Aztec emperor pays tribute to the Chinese, and the Chinese supporting the various frequent rebellions against Aztec rule to punish those Aztec Emperors who pay no or too little tribute. Mostly likely the then-current Aztec ruler tries to get Spanish assistance against the Chinese-backed rebels, maybe even to hire Spanish conquistadores as mercenaries against the rebels and Chinese - which ends with him overthrown and much of the Aztec Empire made a Spanish province - although the Chinese would manage to retain a client/buffer state, perhaps the Purepucha/Tarascans. Or maybe the Spanish only annex some provinces along the Gulf coast and keep the rump Aztec Empire as their own client state and buffer against the Chinese.
Incidentally, once the Spanish land in Mexico, hear of foreigners "from beyond the sea" on the far side of the Aztec Empire, and realize that these foreigners are actually Chinese, it´ll take a LONG time to dispel the misconception that they´ve landed in Zippangu (i.e. Japan)...
I´m not quite so optimistic about the ability of the surviving Central American powers to "westernize" (or "easternize" as the case may be) enough to be on a relatively equal footing with the Spanish; the Maya weren´t fully conquered until the late 17th century, and I haven´t heard of them westernizing their military. Chinese-trained and -equipped formations within their armies, even Chinese "mercenaries" in support of their armies, yes, but no indigenous capacity for equipping their own armies with large numbers of Western (or Eastern) weapons - I think the Chinese would do their utmost to keep the natives totally dependant on Chinese aid to maintain their modern armies, such as by keeping the production of steel and gunpowder a secret. And for the same reason, I do not think the Chinese would teach native powers to build real ships, as they would want to keep them dependant on what the Chinese bring to them, rather than allow them seek out foreign trade on their own.
The Maya will probably resist Spanish conquest somewhat better than historically, and Maya territory from Yucatan down to the Pacific coast will be a loose-ish confederation of city-states that maintains their independence, ably but not altogether altruistically aided by Chinese "advisors".
As for the Inca... since the Zacatecas silver mines are now most likely in Chinese-affiliated territory, I *really* want the Spanish to have Potosi as a source of fabulous wealth, which is in Inca territory. Most likely, the Inca Empire falls at some point, probably later than historically, when the Spanish manage to exploit some sort of civil war; assuming the Inca already had trade contacts with Chinese and Spanish already by this time, both sides probably backed rival contenders in that civil war as yet another set of proxies for a war between them.
Okay... clearly the whole matter needs a lot more thought; I am just making the above up as I go along so far.