are multiple version of the Windows SDK necessary?
Just in case this helps anyone, it appears like the newer versions of Windows SDK installer remove previous versions correctly, but somehow fail to remove their entries from Add/Remove Programs list. In my case, I had as many as 7 entries in there. I sorted them on installation date and started removing one by one, starting with the oldest. For every entry, I just received the following error message:
I kept removing them till I was left with the latest version only. Uninstalling this one brings up proper installer window instead of this error message, at which point you can cancel uninstallation process.
I am posting as an answer here from @magicandre1981 comments above, so I can close the question.
Windows SDK 10.0.26624 is the SDK for the first Build 10240 from Summer 2015.
Windows SDK 10.1.10586.15 is the SDK for the November 2015 Update 1511.
I ended up uninstalling both versions and letting Visual Studio install the necessary package to run my project, which ended up being version 10.0.26624.