To restore your purchase on your other device you need to make sure that the iTunes account that is setup on this device is the same as the one that purchased the app, (to check, open your device Settings (the grey icon), scroll down to iTunes & App Store and make sure your iTunes ID appears in the right hand column).

Please try rebooting the app by double-clicking on the device Home button, swiping the app towards the top of the screen and then double-clicking on the Home button again. Reopen the app, the content should start downloading.