That's really fast! I've never gotten it anywhere near that fast. I'm surprised you were able to defend with just the city defense, actually.
Having a day to think about it, yeah, it was fast. Not optimum, but I have a hunch that nobody will shave more than ~30 turns off of that target.
A few things I got lucky with:
--Choosing my lattice structure. I went with a 1-tile CW offset from the grid. There are three choices available for the lattice, all of which are equally valid on open ground. When you encounter impurities in the crystal (mountains, CSs, capitals), they will remove 1-3 potential city placements. Most of the time, they only cost me one city site. A different lattice would have slowed me down.
--Timing. My early settlers were coming in chunks, because I'd settle a city, queue a warrior until size 2, and then switch to a settler. Without really paying much attention, a few of my policies were available right before I was about to plop a few more settlements. I never waited with a settler on hand...the timing was just clicking.
--Map. It was a good layout in many regards. Pangaea was cut in half with an isthmus, and I got one more maritime and one less opponent on my half than I was due. Discovering 2 natural wonders before turn 50 didn't hurt. The resources were meh...only 2 luxuries in my first 4 cities.
--War. Sully and Monty were my closest neighbors. Sully is a pushover, and Monty never got out of the gate. Sully never even made a strong push with more than 3 units on offense. He took a city a few times, only to lose it right back. I never went on the attack until about turn 90 or so. Four War Elephants and 2 Archers shredded Monty and freed up a ton of open land. He was really just dicking around the whole time.
The city defense in ICS really is brutal, especially if the AI doesn't hit you early. Every tile inside my territory could be bombarded by 3 cities. As long as the AI isn't attacking a corner of my empire, once they take a city on the edge and try to push in, that brings at least 4, usually 5 of my cities into play. Also, it doesn't seem like the -33% unhappiness combat penalty affects city bombardments. Some careful counting of the XP you think the AI units have will also help. Sometimes it's better to spread the bombards around so no unit gets an instant heal and then focus fire on the next few turns to kill them on the same turn they'd get a promotion.
I was playing the game as a lark, mostly just laughing about how obscene ICS could become. It was only about turn 150ish that I realized I might be able to Space Race in less than 200 turns.
After that, I started with some heavy city micro and beaker micro to not waste any overflow research. The research path through the whole game was: worker techs for luxuries in my borders->beeline Colosseum->beelined the next Era->beelined Rocketry->Rocket techs & Railroad. I built the Apollo project in my capital, which took freakin' forever. While that built, I prepped 4 other cities for maximum production (taking control of hills, building mines/lumber), bought Granary/Factory/Hydro/whatnot. My capital built two Boosters. I also got lucky at the very end with Uranium appearing where an allied CS already had a mine. I rushed a Nuclear Plant in the capital to shave the 1 crucial turn I needed off the last part to hit my <200 turns mark.