The Xbox 360 Wireless Controller via Play & Charge Kit is only and exclusively for charging the wireless controller. Play & Charge Kit in this case means that you can charge the controller only on the Xbox 360 and meanwhile may continue playing. The controller inputs are then transmitted to the Xbox 360 not via cable but via radio waves. The Play & Charge Kit is therefore unsuitable to operate a wireless controller with this cable to the PC. This has also been confirmed to me the Xbox Support.
If one uses the cable properly, it works perfectly.