Most PSN games consist of a playable demo, and an unlock file, which are separate downloads. The unlock file is just a few kilobytes, and installs in the game data Utility. There is no icon for it in the XMB after it is installed, so you can't tell if it was already installed. The unlock file doesn't do anything except make the demo work as the full game. You have to download the demo, separately, in order to play the game. Until the demo is installed, nothing will appear in the XMB for the game.