I had a similar issue (installed Win32 x64 on 28/12/2016:
tiled.exe - Application Error
The application was unable to start correctly (0xc000007b). Click OK to close th
e application.
OK
(0xc000007b) = STATUS_INVALID_IMAGE_FORMAT
Using depends.exe I can see that MSVCR120.DLL and MSVCP120.DLL have been installed to
C:\Program Files\Tiled, and are x86 instead of x64 as they should be. Replacing them with the X64 versions allows Tiled to run as expected.
Thanks,
-Reed