First I'm not denying you can win the game by only taking 1 peice on the board (and in 3 turns) or even without taking a single piece (it's possible but never had it happen in one of my games). But all chess is is a WAR simulator, you are at war. Wars can be won with very few casualties on either side, but normally either one or both sides have high casualties. Not to mention in Civ III you can also be at war with another civ, yet see no military action, so your argument of "limited loses" is irrelevent. Chess, the Goal is to kill the opposing King, trapping it and placing it in Checkmate. Civ III you have 5 (?) different victory types, two of which are specifically militarily.
My biggest point is in Chess, there's no Tech trading, you're not facing down multiple opponents on multiple fronts (you can get your units surrounded but it's still theoretically on one front). You also don't have reinforcements (you can "upgrade" pawns but upgrade doesn't equal new troops). Production, Gold, Technological differences, Alliances, Strategic resources, City defense, Citizen happiness, Terrain, or even an RNG in a rotten mood (figuratively), all things a Chess AI doesn't have to worry about.
Secondly my point is with AI, is that it knows nothing which isn't told to it or programmed for it. When I program a program of mine to respond with a screen when I hit "x" is that an AI since it "responded to a programed situation?", no. (yes those were my words, I see I was vague in my explination before). My point was that it's only as good as the programmer, and even if the programmer is a good player doesn't mean that the AI will even respond "intelligently" to a given situation. Coding something for very general situations is much harder then just using your own skills to meet any specific situation in a game.
Also, you can't expect the AI to use something NEW effectively without having to improve it yourself. A big reason why it's a "pseudo-AI." I can't think of a good example right now so let's set back a bit. Imagine if the AI was programed without the use of the current Artillery, maybe a more Civ II'ish Artillery without "bombard" and then it was added without changing the AI. The AI would either not use Artillery at all (because it wasn't programed to use it), or more likely it would build 'em, but wouldn't protect or bombard with 'em (personally haven't seen the AI use Artillery offensively myself actually). Defensively is another thing because it's programed to fortify stationary units, therefore making it "auto-bombard" when attacked (assuming it's defended by a defensive unit). On a simular note, you can't send the Civ III AI to play Chess effectively by just "telling it the rules" and letting it get some practice, let alone being able to do anything at all. REAL intelligence, ie. Human intelligence, can adapt to different scenarios and can learn new things by itself with out being told by someone else. The greatest Chess players in the world learned chess from others learned strategies from others, but it was THEY that learned the ultimate game playing skills. That is what I ment by a "psuedo-AI" it may be Artificial, but it's not inherently Intelligent, otherwise it would be adaptable, and we wouldn't even be having this discussion because it would improve itself after playing game after game vs. you and learn better how to counter your strategies forcing you to adapt, forcing the computer as well to adapt to the changes you've made in your technique, eventually creating the "Ultimate AI" which even the best would be hard pressed to win a victory against (at least given enough experience on the computer's part).
EDIT:
Originally posted by The Last Conformist
One relatively easy way to improve the AI would be teaching it to micromanage its cities to optimize shield, food and commerce production each turn
Would be fairly easy I'd think too, but I think the hardest part would be determining a way to get the AI to produce Goals for each city. ie. "this city I wanna grow right now, this city I wanna get me more gold, this city I want to build lots of sheilds, and this city will be going waah waah waah all the way home when I send my tanks in there"
Okay so that last one is pretty much in the AI already, but seriously, it sounds doable if not done now, but the most challenging thing would be prioritizing and making longterm/shorterm goals per city, it's done on a larger scale as well right now so why not?