It does not download the game when you buy it, but when you try to play it, then it downloads it. be patient.
On a Mac, Airspace is in the Applications folder. So is the AirspaceApps folder, which is the one where all the downloaded games are located.
If you click the green button on the Leap menu, you will see "Launch Airspace". Left click on it and the AirspaceApps folder will open.