By the same way they get all their information... by polling the google play store directly with publicly available information
Eg: Top Grossing in Australia
https://play.google.com/store/apps/collection/topgrossing
App Annie is just a simple service which does a web request as specified intervals and compares and stores data and presents to users in a nice format. Nothing special at all.
And your link there proves my point. The Grossing chart follows a slightly different path if you look at the dates and the deviation
Growth..... Organic?, page-113
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