Update:
I tried the DEMO above in single player and it worked fine. I have a GTX680 and i7-3770K so a lot better PC but the demo was locked to a max of 100FPS which I never dropped below once so it's probably going to run okay if your GPU is sufficient.
I ran at 1920x1440 with 8xAA and every other setting at max. Note that's a 4x3 resolution but the actual game has better widescreen support apparently and if not there's an edit which properly lets you run at 16x9 with only some stretching of the HUD (only the compass is obvious like COD1).
http://www.wsgf.org/dr/battlefield-2
and
https://www.widescreenfixer.org/