You can connect with iCloud using your same apple account.
If that doesnt work and you still have your old iDevice, download something called "iFunBox" (google it). Then:
1. Connect your old device to your computer. Make sure iFunBox recognizes and reads it.
2. On the left hand side, there should be a list of things including your User Applications.
3. Find your game's app. You can either check the drop down list from User Applications or click User Applications and search through the grid of apps.
4. Open the App. It should show a few folders and the app icon.
5. Find the folder called Documents. Copy and Paste this to your computer by dragging the folder into desired location.
6. Hook up your new device to iFunBox. Make sure it reads it.
7. Make sure your device does not have the App open at all, multitask included. If it is in multitask, close it.
8. Open up your App's files and delete all the content inside the Documents folder.
9. Replace everything with the files that you copied earlier.
10. Open up the game and see if it worked.
It may or may not work but it's worked for some games.
Comments
If that doesnt work and you still have your old iDevice, download something called "iFunBox" (google it). Then:
1. Connect your old device to your computer. Make sure iFunBox recognizes and reads it.
2. On the left hand side, there should be a list of things including your User Applications.
3. Find your game's app. You can either check the drop down list from User Applications or click User Applications and search through the grid of apps.
4. Open the App. It should show a few folders and the app icon.
5. Find the folder called Documents. Copy and Paste this to your computer by dragging the folder into desired location.
6. Hook up your new device to iFunBox. Make sure it reads it.
7. Make sure your device does not have the App open at all, multitask included. If it is in multitask, close it.
8. Open up your App's files and delete all the content inside the Documents folder.
9. Replace everything with the files that you copied earlier.
10. Open up the game and see if it worked.
It may or may not work but it's worked for some games.