"This app can't run on your PC" is displayed when running a program
In my case, by mistake I had overwritten the exe file with a 0KB file. And trying to run this caused the same exact message
Well, the above error message (shown in the screenshot) is not very detailed. However, the problem is: using a different architecture than Operating System architecture. In my case, I wanted to (or tried to) launch the x64 executable whereas the OS is x86.
To solve the issue, I had to download the x86 version of the same software (the app), and that worked fine. The confusion arises because Windows 8 doesn't provide much detail for troubleshooting the problem.
Corrupted installer is another cause for this error message. See Corrupted files are the cause of Windows 8 "This app can't run on your PC" error.