If swagfag's statements are true, you most likely cannot do this with MouseMove. 99% of FPS games do not pay *any* attention to the position of the cursor, they listen to the signals coming directly from the mouse.
In order to stop the game seeing the mouse move, you need either a Low-Level mouse hook, or something like Interception.
I do have code though that would let you completely stop windows from seeing the mouse moving, whilst still being able to read the mouse movement data, but you would not be able to use your existing code, because it works on the cursor.
To be honest, the technique used in that code you borrowed is pretty sucky.
I have a version that does not work on the position of the mouse cursor - see
this thread, sample script 2.
If you are doing multi-boxing, you may also be interested in my
AutoHotInterception project, which lets you use AHK code to read from keyboard and mice at a *per-device* level. ie you could have a 2nd keyboard or mouse for the 2nd game, and all your AHK scripts for the 2nd game only take their input from the 2nd keyboard or mouse.