I have a Mac Mini, but I think it would be a waste to put it in a cabinet. You'd be better off building something and throwing it in. With the Mini, you're paying a premium for form-factor, and because it runs OS X. You won't get the benefit of either of those things when using it in a cabinet. You have plenty of space in that huge cabinet, so you can use a larger but more powerful (or larger but cheaper... or both) PC instead. Hopefully, you won't have to touch the OS very often if it's in a cabinet, so you'll never have a chance to enjoy OS X.
I recommend one of the following options:
1. Spend the $500 you would be spending on a Mac Mini, build yourself a bigger but more powerful PC to put in your cabinet, and be happy.
2. Spend $300 on a bigger (and still possibly more powerful) PC, use the $200 you saved to get some awesome artwork and/or some extra nice joysticks for your cabinet, and be happy.
3. Use the Mac Mini as your desktop machine, stick whatever PC you have now in the cabinet, enjoy OS X, and be happy.