Many people will say 'yes it matters' and many would so 'no, it doesnt'.
The thing with gaming mice is not sensitivity, but DPI - which stands for 'Dots Per Inch'.
The higher DPI the mouse can reach, the more precise you can be with it, which is why some FPS gamers will tell you it matters - which is true, but I personally dont find it to be crucial.
Its kind of like the Magnification and Resolution argument - If you have a microscope with 10x zoom (representing mouse sensitivity) but a poor resolution (representing DPI) your not going to get a clear picture. But if you have a microscope with 10x zoom, but also a high resolution, your going to get a clearer picture.
There are other arguments to get a gaming spec mouse though, and these are the mor important ones in my eyes;
1) Comfort - you can get ergonomically designed mice that fit your hand and grip style perfectly
2) Extra buttons - many gaming mice come with extra buttons on them, allowing you to map key strokes to them. This could be the difference between swinging your knife first or getting off a grenade quickly, as the buttons would be right next to your thumb.
3) Other features - such as sensitivity buttons, a nice look, an unlocking scroll wheel, or even in some cases adjustable weight.
All in all, a gaming mouse is well worth a purchase for several reasons and not for high DPI alone.
Hope this helps