How do I save game app data in iCloud?

App data is included in the iPad backup. If you are backing up to iCloud, go to Settings>iCloud>Storage & Backup>Manage Storage, tap the name of you iPad under Backups, then look for the app under Backup Options (tap Show All Apps if you don't see it) and confirm that it is set to On. If it is, the app data will be included in your backup.

Don't delete it. Just restore to your iCloud backup. At the end of the iCloud restore process, iCloud will redownload all of your purchased apps again from the app store anyway, giving you a fresh copy. If the author of this app stores your game progress in the app data that is backed up (which I assume it is), you should be able to pick up where you left off. (But you would have to contact the app author to find out for sure what app data is backed up.)