Apps do not automatically update - you have to initiate the updates. I don't do anything on my iPad until the updates have completed because I like to watch the progress and make sure that nothing goes wrong. If something does go out of whack, I can catch it right away and hopefully correct it before it best worse.
Just some food for thought.
Don't restore the iPad in order to deal with the stalled updates just yet. Try these suggestions first and see if the updates will download ..... But if you do backup the iPad and then restore it from the backup - your game progress should be saved. App data, files and settings are contained in the iTunes backup.
..... Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
Or ..... Make sure that you do not have a stalled download somewhere else like in iTunes or iBooks - a song or podcast a book .... if you have a download in there that did not finish, complete that one first. Only one thing can download at a time on the iPad so that could be what is causing the problem.
If that doesn't work - sign out of your account, restart the iPad and then sign in again.
Settings>iTunes & App Store>Apple ID. Tap your ID and sign out. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Go back to Settings>iTunes & App Store>Sign in and then try to update again. Tap one waiting icon only if necessary to start the download stream.
You can also try deleting the waiting icons - tap and hold down on an icon until it wiggles - the tap the X on the icon to delete it. Then try to download again.
You can try resetting all settings. Settings>General>Reset>Reset All Settings. You will have to enter all of your app preferences and device settings again.
