Alright, let's take a look at your COMPONENTS Hive and WinSxS + CBS Keys to see if this update is present in the Registry or not.
Retrieving the COMPONENTS Hive
Follow the instructions below to retrieve your COMPONENTS Hive and send me it.
Open your Windows Explorer, and navigate to the C:\Windows\System32\Config folder;
In this folder, find the COMPONENTS file (there's no extension), and copy it to your Desktop; Note: If you receive an error message saying that the COMPONENTS file is in use, restart your computer and try again. If the error message persist, let me know.
Right-click on it, and select Send to... and choose Compressed (zipped) folder;
Sorry for the late reply, it seems that the KB2862966 is all over your Registry, so it might be possible to reinstall it. Download the update from the link below and try to install it.
You would have to do a Repair Install. It'll basically reset your system, but leave your files, programs and settings intact, forcing you to reinstall all the Windows Updates.