Can you backup/transfer iOS individual game saves without jalibreaking your device?
Solution 1:
As long as you have a wifi / internet connection, most games should perform syncing with the 'cloud'.
Otherwise, you would need to access where the files are located, usually by some service like: iExplorer and PhoneDisk. If you cannot write to where the game files are stored, then yes, you will need to jailbreak the phone to gain write privileges.
Solution 2:
Yes. If you have a backup you can use the iPhone Backup Extractor to retrieve your app data and then import it to your device.