Unreal Engine won't launch Error code (0xc000007b)

There are a few issues reported in your log, one that interests me most at moment is this:

[ E ]  MSVCR120.DLL

This means that there was an error installing Microsoft Visual C++ Redistributable Packages for Visual Studio 2013. answer has a link to this redist and describes how to uninstall then reinstall it to fix issue:

“You can find it here: http://www.microsoft.com/en-us/download/details.aspx?id=40784. You should check Add/Remove programs to see if there’s another version listed there and uninstall that first. Thanks again!”

If that doesn’t work, you’ll have to try backing up msvcr120.dll in your c:\windows\ system32 folder, deleting original, and then running Visual C++ Redistributable installer again.