Complete Deletion of an App on iPad
Due to the way iOS sandboxes apps, when you delete an app, it along with its data are gone. The only remains are in the App Store purchase history. The iOS security means you can't easily undelete these files via a jailbreak - so if you want to ensure the data gets securely erased, you should erase all contents and settings which will either destroy the key used to encrypt.

Don't forget to delete the app from iTunes on any computers you have and then make a backup of your iPad with the app deleted. That gets rid of two other potential copies of the app.

The game is probably just buggy. You can tell the developer and make sure to mention what iDevice you have, its iOS version, and specifically what the bug is.