Games

If you acquired the game from the App Store, open the app store app, select your previous purchases (click on the round icon in the upper right) and find and re-download the game.

If this was not from the App Store but an on-line game of some sort, you'll have to check with the folks supporting that game.

As long as the game was purchased using your Apple ID, you should be able to re-download it from the App Store. It may or may not ask for your password again depending on your security settings.