If you have an app that the App Store thinks is still installed but is really not installed, you can run this command to rebuild the database and fix the app from showing up as purchased, so that you can restart the App Store and then download / install the application a second time.
/System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -kill -r -domain local -domain system -domain user
