Communism is only significantly better than Monarchy when you get to have a lot of cities, at least around the optimal number for the map. Controlling the starting area plus most of Egypt probably put you right around the breakpoint where Communism starts to take over. It'd be about equal at first, but as Communism got improvements built in the outlying cities, it would pull ahead in economy. Communism isn't an instant productivity spigot; it takes time to build up.
Now imagine what would happen if that same player had spoiler knowledge, and/or got more lucky and scored an SGL (or, heaven forbid, even two)! Ah, the possibilities... :p
Actually, when I said "let's see if anyone can beat that time", I really did include myself in that. It'd been two weeks since I wrote my report and I actually didn't remember what my finish date was. I knew it was in the 1700's but thought it might actually have been later than yours.
What I'm asking myself is why such a someone would ponder switching to communism mid-game but delay that decision because of a war, then never mention it again?
I did mention it again, in the second paragraph on page 6. With corruption already almost zero in most cities thanks to policemen, revolting wasn't going to help anything. I didn't have enough cities for Communism to make up the revolt time and get ahead.
What I'm also asking myself is what an AI does if it scores an SGL - will it always try to rush a great wonder, or will it use it for a broken age of science as well? One way to get a hint at that is if someone by chance catches an AI scoring one...
I keep meaning to check my saves and the replay to see if I can figure out anything towards that end. I'll try to remember tonight.

They didn't rush a great wonder, but I think none were available to them. I'm also not even quite sure if that was indeed an SGL in Egypt's city. Finally, there is the possibility that the Age of Science might not actually be broken for AIs; whatever's causing the bug could be specific to the player.