In the Mac Game Store App, your purchases are all located in the "cloud". The cloud exists so you may access your purchases at any time, and uninstall/re-install games if you are low on hard drive space.
If you have not yet installed a purchase to play, they will show up gray in the listing.
To install a game from the Cloud to your machine to play, follow these steps:
1) Click on "My Games" in the left sidebar.
2) Click on the button to the right that is labeled "Install."
At this point the game will begin downloading, and finish by installing. When a game is ready to play, the button will change to "Play".
If you wish to return a game to the Cloud:
1) Click on the triangle button on the right end of "Play."
2) Select "Remove Game" from the choices provided.
If you wish to HIDE all the games in the Cloud:
1) Go to any games listing.
2) Locate the little Cloud Icon in the upper left corner of the listing.
3) Click the cloud icon to toggle hiding Cloud games.