Just finished my game, coincidently, also in 1565 AD, but through the domination method.
The Map
If it wasn't for the fact that we were told it was a random map, I'd suspect otherwise. Just that one little bridge between the two continents. And only one source of iron, coal and saltpeter on our side of it. Coupled with the fact that our closest neighbour (also competing for that iron) were the Persians. My sympathies for whoever slips up and lets the Persians get the iron first. I don't fancy the chances of having horsemen against immortals.
I was close to making this particular slip up, in that the last direction I explored was south, which in hindsight, giving the starting postion, made no sense. The Persian cities were just steadily climbing up to that iron and I had to quickly pelt a settler down there. But once the iron was mine it was (almost) plain sailing.
The Parsi Wars
Well I just got a load of swordsmen together and invaded, slowly assimilating their cities one by one. But, I wasn't building much settlers, and still had a lot of land around my half of the continent to settle. So the reward of a massive barbarian horde gave no pleasure. As I sent some swordsmen up to deal with this, some more barbarians came in from the south. And then another barb warrior (from a barb village, not a hoard) destroyed my link to the iron. Then the Persians retook Persepolis. This, understandably, didn't go down well. But it was just a minor setback, and within a few turns I had re-grouped and the war was able to continue, with no more hitches.
I left the Persians with one town. I kept the one that they had conveniently built on the land bridge. (Can't remember what it was called, but for arguments sake, I'll say it was Susa). And I built a new town a few spaces north of Persepolis in which I started the Forbidden Palace.
The Chinese Conquistadors
I garrisoned most of my army in Susa to keep an eye on the Aztecs. And not a few turns after the Persians had been spared mercy a group of Aztec jaguars, swordsmen and archers were seen coming my way. In a pre-emptive strike I killed off their attack. Now it's worth pointing out that the Aztecs culture was far in advance of mine, and that they (by the looks of it) had greater production power, as I still hadn't gotten round to filling up the rest of my land with cities.
Anyway with my swordsmen I managed to take their nearest (and most southern city), but due to their massive culture, they had it back in a few turns. A new strategy would be needed, but fortunatly I was a few turns away from getting Chivalry.
Just as I was about to get my first Rider kill, and a subsequent golden age, the Aztecs sued for peace. Normally I would scoff in the face of such cowardly deeds, but my production was still not good enough to overcome theirs. Also the Persians were beginning to build cities in some of my leftover land. So I killed off the Persians (getting my golden age at this point), and finished building my cities during a brief spell of peace.
By now my science rate was beginning to out-grow that of my enemies. I had a mighty army of Riders ready to put the Aztecs to the sword. The Aztecs declared war and the Never Ending War began (or NEW I, for short, which could also be related to the NEW world order.

), for not a few turns into the war the Zulus joined forces with the Aztecs - the eventual cause of their demise.
My riders swept into the barbarian continent, and put flame to the great Aztec cities, (There was no point in taking them over as culture flipping was too great a possibility), except the former capital, Tenochititlan, which was kept as an outpost, a resting point for tired and valient warriors.
In a turn of shockingly good fortune my first great leader emerged from the dust of battle. He was immediatly sent to complete the Forbidden Palace, which, even through a golden age, had failed to show ant signs of nearing completion. This new development catapulted my production into the stratosphere. Any doubts as to a Chinese victory were cast aside.
Then disaster. The Aztecs learned the secrets of gunpowder. However this calamity was short lived as my scientists/slaves discovered the secret of the military tradition. All riders were sent back to the nearest town to learn how to master the arts this new learning provided.
From here on is uneventful. All Aztec cities destroyed, and all Zulu cities, with the exception of one hole in the middle of nowhere, to lead as an example to what barbarian cultures produce.
All my cities then began to churn out settlers to fill the gap war had created, and to bring proper culture to the refugees who littered the land.
In a few turns domination was mine.
Also this was my first ever game as the Chinese. The Riders are amazing (though I still prefer Immortals).
I also got a total of 6 great leaders throughout, possibly my best so far.