What do you mean? Im not sure to understand. If you press the middle mouse wheel button and move the mouse around it does not rotate the camera for you?

It works perfectly fine here. I suppose it works for most people. I would try to solve the problem on your end. Does the middle mouse button work for other applications but only does not work for galciv 2 and 3?? That sounds strange.

Wait, you know that the mouse wheel can also be pressed right?

You can try unplugging the mouse, pourring rubbing alcohol over the wheel so it seeps in the cracks then mash the button with your fingers. With some luck that might clean it.

Just wait till it dries before plugging it back ( I.E do it before going to sleep )

If you are feeling a bit more technical you can also unscrew it to do more of a precision job.

Just make REALLY sure there is no liquid in the mouse when you plug it back, you do not want the thing to go Shorty shorty.

Rubbing alcohol is quite volatile, you can blow canned air once you are done to help remove excess liquid. I can get the 99% ethanol here, it is my favourite to clean all sort of electronic.

Given that the button for the wheel is generally to the side (so drenching the wheel wouldn't hit it anyway), and the switch is more likely worn and broken than dirty, I'd save the alcohol and just buy a new one. The actual contacts are sealed inside the switch so the only thing crud could do is prevent the lever from moving smoothly. If it clicks as expected, it's moving just fine.

"Alcohol works wonders most of the times", well I can't argue with that.

Your typical microswitches are not hermetically sealed. You can spray inside them with contact cleaner spray usually from around the button opening.  I agree  the chance of alcohol getting to seep inside by pouring it on top of mouse openings are very slim.

I guess I should not have suggested that, but not much to lose if OP was going to buy a new mouse anyway.  Personally I would just open the mouse and clean the switch directly, It is worth a shot. 

Hell, simply mashing the button energetically might do it.  I have seen dead switches and bad solder joints of course, but very rarely compared to dirty switches. I have never seen a mouse with a bad switch, dirty mice and broken cords, yes. But not broken switches.

However I recently replaced all the microswitches in a vintage Roland synthetiser, about 50 in total. Even after cleaning they still worked badly. But it was this type of button, those suck.

Now I am curious about what OP did, hehe.

The screws are usually hidden under stickers. The idea is that it voids the warranty of you pierce it.