I understand this is vague on purpose but wish there was more detail. E.g., if I am running a game in a webgl canvas and "back button" has meaning within the game UI which I implement via history states, is my page now going to be demoted? This article doesn't answer that at all.

Your game probably has poor SEO to begin with, so the Google Search policy changes would not apply

If it automatically adds something to the history when you visit the page, then yes. If it only adds to the history when the user clicks something, then I would assume it would be fine. Hopefully.