Promotional Game - royalties?

I am considering making a promotional game for paid non-game media, specifically a book into which it is sort of a tie-in that would be completely free, and might most likely also contain a button to redirect to a website for people to find out more & get the actual book, but there would be no way to purchase anything including the book inside the game, I couldn’t reliably directly track purchase decisions to the promotional game either, and the game itself would be free (not tied to buying the book to get access or anything, and the book doesn’t unlock content in any way). In addition, I might also promote my patreon inside the game via external link, but again without allowing any sort of purchase decision right inside the actual promotional game.

Do I read the terms of use correctly that since no direct purchases of any kind are tied directly to the app, and it’s free and doesn’t NECESSARILY lead to the other things being bought outside of the game (and I couldn’t tell for sure for the cases where it might) that as a result, I also don’t need to pay any royalties? I just want to be sure I got this correctly

You wouldn’t owe royalties on a game that’s free that is promoting something else. You would only owe royalties on revenue that the game itself made.