Sadly, I don't think the MacMini can play this game either. It will become very frustrating very fast.
I just purchased (and took back the next day) a Solo core MacMini. 1.5ghz 667Mhz FSB, 512MB ram. (I havent had an Apple/MacIntosh since my Apple IIe and Apple IIgs days <---still may favorite all time computer. Hey, no hard drive, but it had color graphics & sound

) Anyway, I wanted to be able to at least play 2 games on it. WOW and Everquest. I loaded and tried Everquest and it was unplayable. I'd rank it a 3/10 on playability. Now, I know I should have had at least a gig of ram, but I turned everything down, and it was still unplayable. Heck, Everquest was released in 1999 7 years ago and the MacMini still couldnt handle it well. The MacMini for the price I paid just wasnt up to par and didn't do justice for what I expect a Macintosh to do in 2006. Great for a 2nd computer, attaching to your TV as a media device, or for children to learn with etc..but no way for 3D games. It might be possible for the dual core MacMini 1.66mgz to give it a go, but I'd say that would be the bare minimum.
After returning the Solo, I decided to get a laptop/macintosh combo which were 2 things I always wanted anyway. So I got the MacBook Pro 2.0ghz (Funny, the lower priced 1.83ghz wasnt avail. Apple thought everyone would buy the 2.0 instead so they shipped plenty of them. Yeah right, its $500 bucks more). Specs: MacBook 2.0g, 1gig ram, 667 mhz FSB and ATI Mobility Radeon x1600 128mb GDDR3.
It plays Everquest fine and I'd rate it a 7/10. Just a touch of lag but playable. I think this would handle Civ IV good enough. (Haven't gotten to try Wow yet, the servers were down this morning).
My main computer currently; 3.0ghz Hyper-Thread IBM comp, 800mhz FSB, 1gig ram, ATI x850xt 256mb GDDR3, plays Civ IV very well and I'd rate it an 8.5/10. It gets a little boggy/choppy later in the game but very playable.
CIV IV is a beast of a program. Its harder on my machine than some 1st person shooters like HalfLife 2. No joke. CIV IV will expose your machine if it's lacking in any way by today's standards.