[iOS] "This item is for an app that was purchased by a different Apple ID. To Buy this item with this Apple ID you must first purchase the app"

What's happening here is that someone else has downloaded the game onto your device with their apple ID and this is why you can't make any purchases with your apple ID. If you would like to use your apple ID then you will need to delete the app, and download it again with the same apple ID as the one that you want to use. Or alternatively use the same apple ID login as the one that was originally used to download the game onto the device.