Thanx for congrats, but this result can be improved. I didn't manage GPP properly - enough said I had my GPP city with GLibrary, which gave me 4 useless GScientists - nor slavery, so if anyone wants to improve - you're welcome!
The main points:
0. Marathon speed as it's dates in the relevant range of 15-17 centuries correspond to greater number of turns made.
1. Arid world with high sea level to leave computers minimum living space.
2. Pangea to meet soon everyone for trades, religions' expansion and efficient research.
3. Inca to destroy some of them soon and grab land to build 9 cities for 3 cathedrals of each faith. Also starting Mysticism gives good chances on founding either buddhism or Polytheism yourself.
4. Extra rivals (less land per civ - slower research).
5. 1-2 brain-dead aggressive rivals thrown in a tub of peace-monger wonderfully divert them from religion-founding and wonder-building. Ideally they should always be at war with peaceful. Unfortunatelly, Monty was my neighbour and lost me 2 wars, but slowed down my religious development.
6. Starting forested hill for Quechua churning, either gold for research and empire upkeep or stone for pyramids. I had first at Cuzco and both 1st and 2 nd at Delhi - the first city I captured.
7. Attack with 5 quechua as soon as you get them to the battlefield. If fails - rinse and repeat

. Had to do it 4 times after year 1000 BC until got this victory.
I founded Buddhism and captured Indian cities with Hinduism and Judaism and worked tiles of gold, corn, and stone.
An important note - not all people seemed to know it, but at Deity level somputer workers improve land twice as fast as yours. Thus, if you're going to capture a city, you'd better not steal workers but allow them to quickly improve "your" land using techs you might not have.
Then I saw I had no Marble or Bronze on the territory of 2 empires. I saw Marble captured by Egypt, they had excellent land once one gets IronWorking, so I pumped more quechua and got all their cities. Thus 8 cities were captured and none razed. During the whole game I built just 1 city - Cuzco.
After the conquest I had to crawl for pottery, as my upkeep was killing me (negative at zero science). Then, with cottages and financial trait the situation became to improve. Masonry and stone and much preliminary chopping gave me Stonehenge and Pyramids, I switched to Representation for extra 2 happy faces. Oracle allowed CoL-slingshot and Confuciaism, further research gave Philosophy and Taoism.
For border defence accumulated on most "tank-threatened" direction axes and allowed Monty to kill half his army on my defences, brought in war ally, each destroyed one of his cities.
Then I had good relations with all peacemongers - same religion with Fred and Cyrus, cautious Musa, made some trades and gifts, but not too much and
avoided giving away happiness resources to limit rival growth. War-mongers were smashed and under control. I switched to OrgReligion and, once I happiness from Calendar, USuffrage. Once I reached Liberalism (took Printing Press) and Nationalism (Hermitage) with Gunpowder for safety, I started to accumulate money instead of spending them - my mistake. I built and purchased missionaries, temples, monasteries (at 3 cultural cities) and cathedrals. Timely Engineer allowed me to get Taj Mahal in Cuzco. Then as nearly all was done, I switched to 90-100% culture trying to get GA in 2 cities. Suicide attack by Aztec was thwarted and their cities captured. It might not be wise for cultural victory, but I tried to save Tenochtitlan with HG and spent 1 GA for culture bomb. 5GA in 2 cities blown cultural bombs - and that was it.
Due to constant fight between AI and unfovarable land I managed to build myself:
Stonehenge
Pyramids
Oracle
Parthenon (for GPP)
Sistine Chapel (for culture from specialists)
Colossus
Taj Mahal (by Engineer)
The technical lead when I started to accumulate money was sufficient to gain victory of any type - just research Military Traditions and get Cavalry when noone had Guilds or Paper.
All in all, that was a good game, but still has enough improvement opportunities.