A while ago itch.io started showing (Google) ads to visitors who aren't logged in after downloading a game. Maybe they're now shown in more places, but even so this sounds very intrusive.
Personally, it seems more like a bug, since the page displaying the ad always does, while others never do. If it were due to a policy change on Itch, the ad would appear randomly on any page, and that doesn't seem to be the case.