When I started the installation of VS 2013 in my Windows 8 then I got the warning message at the end of the installation dialog Windows Store app development requires Windows 8.1.
Well, you have no other choose but to install Windows 8.1. You will no longer see the warning message when you retry to install VS 2013.
You will have your VS 2013 without any issue.
God bless, the JSON passing between the Web API and JQuery did not break. So all the code below are still working.