I love the Civilization games, Sid Meyer and I must think somewhat alike, because the system for victory in the games suits my taste well! That being said I have a confession to make, I got the wrong game for the sake of the class, I ended up with Civilization Evolution and not Civ III. However, I was able to find a goodly length demo for Civ III online (Thanks Gamespot.com) and played it and found that in the elements of the game that apply to the question are very similar in both versions of the game, so I think I can still accurately answer the question well.
This game appeals to the gamer with more than simply the story line (which is pretty weak compared to some of the huge scale RPG games there are out there), instead the gamer’s attention is kept by the the way the game is moved along by making decisions based on the parameters and special skills that each Civ has and what kind of victory you are aiming for. For example, I have usually, in the past and for the sake of this project, chosen Montezuma and the Aztecs. Why? Because when I play games like this and Risk, I like to rule with an iron fist(!) and the skills the Aztecs start with lend well to my dominating nature and make the end victory easier. Honestly, I have never played any of the other Civ games and made it to the space age, I always seem to get impatient and win by domination; I just amass most of the land in war and win that way around the late Middle Ages. I have tried to build my libraries and temples and made my wonders, but in the end I just kill everybody and win that way (I feel like a "Mwahaha" should go after a statement like that!)However, for this project I tried playing with a Civ that has starting abilities that do not work as well with a war victory, like the Egyptians who have religion and masonry, to try and make up for my lack of patience and build up my Civ for a cultural victory. I didn't get to finish this way, but it is a way to make the game involve more strategy and adds another level to gamer interactivity in the way that you make the decisions that determine what kind of win you hope to have. It is this very thing that endears so many fans to this game; there is a way to beat the game that will appeal to everybody’s taste; whether you are like me and want to rule them all, or if you want to win through scientific or cultural advancement, there is a game strategy for you. This is accomplished through the individual “skills” that each Civ has at the beginning. For example, my favorites the Egyptians, are considered to be religious and industrious, so they start with skills like clay working and get bonuses for religious endeavors. Other civilizations are considered scientific and start with skills like written language and others considered expansionistic, so they have bonuses for exploration attempts.
With the various styles of Civs and the multiple ways to win, this game offers the player a chance to build and fine tune their civilizations in a way that appeals to them. Sometimes your efforts are successful and your nations will flourish, other times you will be destroyed by your own hubris (I have bitten off more than I can chew several times and paid the price for attacking a nation that had superior troops or just more of them!) Sid Meyer has found away to appeal to several kinds of gamers with more than what games like Risk can offer. There are ways to win that will appeal to those that want to win through careful strategy and hours of small, deliberate moves (like the space race victory), and you can just take over everything to win for those like me who have no patience and want to win with a crushing blow to my enemies so I can see them driven before me and hear the lamentations of their women!