That video is quite long so I've bookmarked it for later. Besides, I fear that it will give me a strong urge to play Civilization 3 again, and I have enough games that I want to play already! While Civ 3 has several things that could be criticized I never found the AI to be one of them, except for being generally dumb of course, but compared to the AI in Civ 6 and 5, it is a genius.
It is interesting how much Civilization fans favorite games differ. I think it is a good testament to how good Firaxis and Microprose/Meier have been at keeping focus on what makes the games good, and of course some luck as well.
I think Civ 3 is the best game in the series, while Civ 5 is number two. I can certainly find several aspects of those games that could have done better, but I don't necessarily think that the most rounded, well-balanced and polished game is the best one. Civ 4 is obviously that in the Civ series, and while it is a magnificent game, it doesn't quite reach up to 3 and 5 for me. (But if you add in mod support, 4 obviously beats 5 to shreds.)
For number 3 it is certainly true that corruption wasn't the best way to restrain rapid expansion. (While also many times better than the Civ 5 approach.) Civ 4 did this best as you mention. But after I read about how corruption works in the game (on this site) I never had a problem with it in the game, and I was able to plan around it. But like many other aspects in many other entries of this series, it should have been explained clearly in the Civilopedia, and not be something you have to actively look for on a fansite to be able to understand. A negative aspect about Civ 3 corruption is also that it is so important for your development that you plan your choice of governments around it. So in the mid game you will either use republic or monarchy, which is as intended, but in the late game you will either stay with republic or choose communism. So neither democracy or fascism are ever very good choices, which is a shame. (Civ 2 got the government balance best.)
I will watch that video with interest later, though I suspect that I will disagree about parts of it too. I actually like both approaches towards AI opponents in theory. (AI "trying to win" so actually an AI that simulates a game opponent and an AI that tries to simulate another civilization/nation state.) Both approaches could be bad if they were taken too far in one direction, but otherwise I like that this series has tried out different approaches. I suspect that I am a greater fan of an AI as a simulation of another civilization, because pretending that I am watching real (alternative) history is something I enjoy a lot with this series. On the other hand I do also enjoy the "competitive" aspect of this series a lot, where I develop grudges towards other civs because of border issues, wonder issues or global diplomacy. Or "friendships" or alliances for pragmatic reasons or just because I want to have a good relationship with a certain Civ.
The advent of the "immortal" leaders was a very good choice of Meier in the first place. While it made the job of the simulation aspect of the game harder (you have to imagine that the leaders aren't really there for the whole game, when in fact they are), it also gave the rival civilizations a personal touch that probably has been important for the series.
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