I am not the ideal person to answer this, but I used to work in a store selling Wintel games. From my experience there, the minimum requirements on EA games was questionable. Usually the minimum they stated would just about be enough to get the game to load without crashing out to windows, and while playing you'd get no more than about 10fps if you were lucky. Usually you'd need at least the recommended requirements to play the game to a satisfactory standard.
I don't know if this is the same for Mac games, but I'd imagine a Mini that is not much over the minimum requirements would run it okay but not ideally. It's up to you.
I run UT2004 on my iBook which isn't much over the minimum req and only just has a graphics card good enoguh to run it. It runs okay with all the settings at average and the resolution at max (10224x768). I can get about 20-30fps as long as there aren't too many bots (I only play 1 player!). I still get a lot of enjoyment from the game like this. Judging by the size of your monitor, you must run 1600x1200 right? I imagine this would be pushing it. The framerate might get very choppy at this size. I'd recommend 1024x768 windowed for optimum performance fps wise.
I must say actually that Tiger has made a big improvement to the OpenGL drivers. My iBooks performance on UT2004 is about 60% better (going by framerate), so if you're gonna do this, I'd recommend running Tiger. 10.4 that is. lol how confusing.
Hope this helps in some way.