Apple - How can I reinstall an application that the Mac App Store thinks is installed already?

Awesome, I figured it out. Run this command, which rebuilds LaunchServices:

/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user

And everything should be back to good! Immediately after running, the App Store allowed me to re-purchase the app.

Source: MacLife Link

Just hit Launchpad and delete your app there by clicking and holding down the mouse button and clicking the "x" top left.

Now the Mac App Store knows it's deleted. Just redownload and be HAPPY!