Game apps are stuck in download mode. How can I delete them? When they shake there is no x in the corner to delete them.

Delete the download and re-download it from the app store.

Select the game icon and keep pressed until it starts to shake.
You will see a tiny delete on the top left of that icon. press that to delete the game/app How to Delete Apps on iPad and iPhone How to Move Icons on iPad Organize...

I found a blog about this phenomena here: iPad Screen Shaking Issue

Which app are you trying to delete? The are certain system apps that cannot be deleted which include, Photos, Clock, Map, Music... to name a few. These won't have an "X" and cannot be deleted.

you cannot delete them:
there are some core apps belonging to the iOS system and cannot be deleted like 'clock', 'calendar', 'contacts', 'facebook' etc.
- however you may create a folder (unwanted apps) and put them there, then they are at least out of sight and use less desktop space.....
1) Airdrop
2) Apple Store
3) calendar
4) camera
5) clock
6) contacts
7) facebook
8) game center
9) iBooks
10) iTunes
11) mail
12) maps
13) messages
14) music
15) newsstand
16) notes
17) photo booth
18) photos
19) reminders
20) safari
21) settings
22) siri
23) tips
24) touch ID
25) videos
How to create Nested Folders in iOS 7 Video

it is one of the most basic things to know for iPad owners:
icons (or Apps) will be deleted if you press for some seconds on it and after it shakes you may delete it in pressing on
What needs to be done to remove an iPad application:

1. hold on to the icon that you wish to uninstall.
2. After some seconds continous pressing, the App icons will begin to shake.
3. Then tap the close button which will be denoted by 'X' symbol on the top left corner on one of the icons you wish to delete
4. You will be prompted whether to delete the application.
5. You will have to click on the delete button.
6. If you wish to re-install the application later again, you will have to go to the App Store and then download again.

How to Delete Web Page Links on the iPad

It is one of the most basic things to know for iPad owners:
icons (or Apps) will be deleted if you press for some seconds on it and after it shakes you may delete it in pressing on
What needs to be done to remove an iPad application:

1. hold on to the icon that you wish to uninstall.
2. After some seconds of continous pressing, the App icons will begin to shake!
3. Then tap the close button which will be denoted by 'X' symbol on the top left corner on one of the icons you wish to delete
4. You will be prompted whether to delete the application.
5. You will have to click on the delete button.
6. If you wish to re-install the application later again, you will have to go to the App Store and then download again.

How to Delete Web Page Links on the iPad

Sounds like a rubbish app/game. Delete it.

If you like the game download it again and see if it behaves properly this time.

(apps/games are cheap/free for a reason.)

Good luck.

Sounds like a problem with the App itself. You may need to delete it and re-install. However if this is a game you will lose your progress. Best to contact the app developers directly.