IOS – How to remove iCloud data for a specific app

The answer is yes and no.

What happens quite easily after a restore (for example after an update) is that iTunes restores the save data for all applications, but not the applications themselves. Therefore as soon as you install them, the old save games will be available (this applies to all apps, not just games). Just by itself nothing will be saved without backup.

BUT: If the application supports iCloud sync and stores it's data in iCloud (which has to be explicitly supported), your data will be still available after deleting and reinstalling the app.

In short: You should be really careful and unless you're absolutely sure the application in question does support iCloud for your saved data, don't delete it without backup.

The direct answer to your question is It depends.

Certain applications like iWork can store data in the cloud which is then synchronized across devices. However there is currently no interface to allow you to choice which document is the primary, as the data is synchronize on a last updated cycle.

If the game support using shared document via iCloud, you would be able to synchronize game data, however, by default it will not.