Binding that button to "middle mouse button " using the Logitec control panel is the only way I have ever got a middle button function in games.
Your mouse hasn't got a 4th button that could be changed to "close application"?
There could be a keyboard command for closing apps but not as handy I know.
Right button works as alternate select in Windows and mouse2 in games,so maybe write to Logitect about it and see if it can be done(maybe in the next drivers).
I have logitech dual optical and I had the same problem. You need to check the two boxes in the scroller option then you should be able to use the scroll wheel in your games.[different setups vary] Image attached.
I have both the scroll boxes unticked and used a patch from Logitech called "game_whl" that makes the wheel work in games
ie weapon change in Quake3.
The wheel funtions as it should in Windows as well so I didn't try ticking the boxes (maybe the wheel fix is in the drivers now).
Ep, glad to see you come back and tidy up...did want to ask a one day favor, I want to enhance my resume , was hoping you could make me administrator for a day, if so, take me right off since I won't be here to do anything, and don't know the slightest about the board, but it would be nice putting "served administrator osnn", if can do, THANKS