I haven't found a way to run it in windowed mode, but (for me) I've found something better. By setting DirectDraw=0 in the .ini, the game will launch in what seems to be borderless windowed mode, using my monitor's full 1680x1050 without doing any sort of stretching. There are some black areas in the bottom of the UI since the UI wasn't designed to cover so much real estate, but it's a beautiful playing experience. It seamlessly switches focus to other applications without breaking anything.
FYI, you may have to start up the game at least once (and endure the painful monitor resizing and wonky colors that result) in order to get it to generate a "Alpha Centauri.ini" file before you can add directdraw=0 to it.
EDIT: it's not a real borderless windowed mode, as it won't minimize properly, but it's otherwise perfect for someone like me.
This only works with the Expansion Pack installed, for the record.