The great thing (ahem, one of them) about Civ III is that is so flexible. You can play it so many ways, and with so many styles and strategies, that it never really gets old. It is unlike most games, which offer cheap thrills, heavy adrenaline, and 1000 clicks/minute (things which older people do not usually enjoy). I can't picture myself ever growing too old to enjoy launching a space ship, or finishing the Great Library, or conquering that last German city with 17 defenders in it...
You can play it for 10 hours straight, or for 15 minutes, or anything in between. This mass appeal and flexibility mean most addicts will probably never get "too old" for it. It is a thinking game which only appreciates with time.