Apps not appearing as installed in App Store
Applications installed on your system that are available in the Mac App Store should be labeled as Installed, but some people are finding this is not the case.
When you have applications installed that are available in the new Mac App Store, the store should show the application as being installed instead of having an option to purchase the application. Despite this behavior, some people have found that applications they either have previously installed or have downloaded from the App Store are not registering with the store and have a Buy option next to them instead of an Installed status.
If this happens, one reason might be if you have moved the applications from their default install location. Try moving them back to the Applications folder to see if they are properly recognized.
This issue may also be from the App store not being able to fully access the installed application packages, since some people with this problem have found that changing the ownership and permissions of the applications has fixed the problem. Go to the applicaiton in question, select it, and get information on it (Command-I). In the information window, look at the permissions and be sure they are similar to the following:
Ensure the first entry (the "owner") is set to either System or an administrator username, and has both read and write access.
Next ensure the second entry (the "group") is set to "admin" or "wheel" and also has both read and write permissions.
With these permissions set, from the gear menu select "Apply to enclosed items" so the permissions are propagated to all items within the application package, and try checking the program again in the App Store. If it still does not work then go back to the information window and set the Everyone group to both Read and Write from the default Read Only permissions, and again apply the permissions to the enclosed items for the application.
If the store now properly recognizes the applications, you might want to revert the permissions for the Everyone group back to Read Only if your system has managed (nonadministrative) accounts on it that are used by people other than yourself. If you are the only one using the system, then this setting will not matter unless you have your Applications folder shared on the network (there is likely no reason for this).