Linux doesn't run .exe files unless you have Wine or something similar. Anyway, Windows drivers would never work on Linux. There are specific drivers for every different kind of operating system.
Proprietary drivers are usually kept up-to-date in Ubuntu under "Additional Drivers" (you can load it from the main menu or by searching for "driver" if you use Unity). Check there first to see if the most recent Fglrx driver is turned on.
If you still want to install it manually, go to AMD Support & Drivers and enter the values of your system, and you will given a .run file, which is a bin file and will work just fine.