Okay, I have confirmed your same issue on the my Due. As a comparison I tried the KeyboardAndMouseControl on my Leonardo and it works fine.
One thing I noticed as I watched the Windows Device Manager when I plugged in my Leonardo it was detected on one COM17 port which is used for the programming, but then after about 5 seconds it re-detects on COM18 which is used for serial comm. But in addition it also installed a USB Human Interface Device.
The Due does not do this. Which leads me to believe the Arduino Due driver is not supporting this feature yet.
Anyone else knows if this is true or not?