If you haven't used Appirater, the article doesn't make it clear that one way to use it is to only nag users for a review after they've hit a "significant event" like completing all the levels or improving their score or whatever.
I did exactly this in one of my android app. When the user successfully finishes the games, he will be given an option to either rate the game on Google play or retry the game again. If he fails to complete the game, he will just be allowed to retry/quit.