Oh, also:
(3) Completed games in non-daily tournaments do not cause a "Review your game" notification in the "Play" popout menu. Or at least do not always cause one; I think it never happens, but I could be misremembering, so maybe it does happen sometimes.
These have both been going on for a while (weeks, I think), at least on desktop:
(1) If you review a game starting from your game history instead of from a notification in the "Play" popout menu, that will not cause the associated "Review your game" notification in that popup menu to go away. To be clear, I don't just mean "immediately"; I mean it will still be there even after refreshing the page, going to many other pages, et cetera.
(2) In some cases, your game history will not show the "Review" link even though you've never reviewed the game. I am not exactly sure when this happens, but it happens a lot, at least during non-daily tournaments. Maybe it has something to do with things you might do from the tournament page while your most recent game has finished but before the next round has started (e.g. looking at the standings, or ongoing games, or whatever).