I think I see the problem now. We have the web installer, which is what your first screen shot shows in which VS 2013 is missing, and we have our standalone installer
. When you go through control panel add / remove programs it's using the stanalone installer (which the web installer downloads then launches in silent install mode). I've asked my QA team to verify this scenario.
Did you let Change finish? Is it working in VS 2013 now? If not I recommend uninstalling, then downloading and running the standalone installer.