1) - Open game
2) - Click "Mods"
3) - Load ModWarfare
4) - /Record & /Demo demoname
If you record your demo without changing your mod first, you will have to exit the game and move your demo from Main/Demo to ModWarfare/Demo.
You demos should now play.
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Visual Demonstration by St.Anger
Ok, hope you'll get it this way..
Move the demos folder to your MODWARFARE folder:

Start the game a select mods:

Select ModWarfare and press launch:

Start your demo:

Don't know how else to explain.. If it still don't work post console (~ ingame)