Hi there, Kingtiger ! Something like that happened to me a couple of weeks ago.
I had purchased COD4 in the App store, and somehow- cant remember well- I went to the App Store, found the app COD4, clicked on install or play, then it asked for my Apple ID. I entered it and that was it.
I tried so after reading this:
https://discussions.apple.com/thread/7335191
Hope this helps.
Best,