Hi Derek:
I'm not sure. Are you saying you put the patch's icon on your desktop?
Well, there's an easy way to find out. Take the CD out of your drive. You don't need it to play EU2 anyway.
Now, doubleclick.
If it's the patch, then it should install normally. Just follow the directions and make sure it goes into the right directory. (The same directory your EU2 files live in.)
If it is trying to reinstall the game, then it's going to give you a 'CD not in drive' error. Just hit cancel.
Your best bet is to find where the patch was saved on your hard drive, and double-click it manually.