You actually get a notification, similar to the one when they make a move. Not the little icon at the top but a yellow notification box.
Finished Game Chats

You actually get a notification, similar to the one when they make a move. Not the little icon at the top but a yellow notification box.
I thought so too, but I just finished a game where my opponent resigned. I not only did not get notification of his resignation (I noticed our game went from a current game to a finished game) but when I viewed the finished game to see what happened, I saw his chat, for which I also did not get a notification. All my notification indicators/switches are on, so it isn't that.

Maybe if the chat is made after the game is over (mate, resignation), no notification is sent. This doesn't explain why I don't get one when a game ends. Now that I think about it, I haven't got a notification for a game ending for some time.
I just found out that if an opponent leaves a chat after resigning, I won't see it unless I view the finished game and then click chat. I wonder how many I have missed and how often my opponent might have considered me rude for not responding.