It's been awhile since I used that in AppGameKit but it appeared identical to the
iRate library, and I suspect that is indeed what is used on the backend (or an earlier precursor of it). With that, it stores the session data to a local settings file (e.g., User Defaults) and when the user opens the app so many times or so many days have elapsed it prompts them to rate it. If they do a full uninstall of the app and then reinstall, they will be prompted to rate again.
Sadly, the AppGameKit version does not provide the configuration options that iRate itself does. You cannot specify precisely when to prompt the user, or how long it should wait before prompting again if they select "Ask Me Later."