Do both device use the same Apple ID? It seems that the game progress is tied to that ID and maintained on the server vice on the iPod itself.
Have you contacted the developer? I do not see that question/answer in the developer's support site.
Create a NEW account using these instructions. Make sure you follow the instructions. Many do not and if you do not you will not get the None option. You must use an email address that you have not used with Apple before.
Creating an iTunes Store, App Store, iBookstore, and Mac App Store account without a credit card
You may have to create a new ID and use that ID to purchase the app.
If you have to create a new account you can ccreate a NEW account using these instructions. Make sure you follow the instructions. Many do not and if you do not you will not get the None option. You must use an email address that you have not used with Apple before.
Creating an iTunes Store, App Store, iBookstore, and Mac App Store account without a credit card