Personally I find it quite annoying that we're being forced to use 360 controllers in many of these "games for windows" releases. Purchasing a receiver so I can use the 360 controller on my PC when I've already purchased a decent normal gamepad doesn't seem practical. I could just use the keyboard and mouse of course but on some games I prefer using a controller. Thankfully there is a piece of software which allows me to do just that. It's a 360 controller emulator called x360ce. I assume it works by translating the directx input from your typical controller into whatever the game is expecting from the 360 receivers input. x360ce works for other "games for windows" games by renaming the included xinput1_3.dll file to one of the 4 possible variations the current games look for. The file names are listed below.
You may also have to edit the file x360ce.ini to remap your controllers buttons or analog sticks to better suit your preferences or correct misconfiguration. My PS2/PC Alienware controllers left analog stick was inverted.
For Just Cause 2 download the x360ce 126.96.36.199 file available in the right hand column extract the files and copy xinput1_3.dll and x360ce.ini to the games installation folder. Prior to copying the files you can test the input using XInputTest.exe