It is up to the app developer whether or not game progress is saved in backups. Most games are saved, either in the backup or on the game provider's website. If it is a multi-player game it is always saved in the provider's cloud.
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We learned this the hard way. Make certain that you have created a gamrecenter login/passcode in your settings. Backups do not save the progress. Only the actual app. This may be different for some apps but my kids lost all supercell progress when their ipad broke and we used a backup on the new one. And it is nearly impossible to get supercell to help you.
Make sure you set up gamecenter!!
Question: Does iCloud back up back up supercell games such as clash of clans and progress?