I can think of a few game properties that aren’t entirely covered by mechanics if that is what is meant by this.
There is at least one game in which Schadenfreude is at least half of the point of the game and that is 6 nimmt. Usually, I’d say Schadenfreude is not something I want in a game I play. But 6 nimmt manages to make it hilarious because right after you laugh because someone else has to take a row, you are the next one to loose all those points. I am not sure I know of any other game that manages to make this particular emotion feel “okay”-ish. Caveat: I’ve only played the BGA implementation recently and this makes the game really quick and without any fiddly counting and moving cards etc for any player involved and maybe this helps along making it more hilarious than it might be on the table (it’s been many years since I’ve had it on a table). This is not to say this is a favorite btw.
The following 2 definitely are favorites of mine.
Another one that comes to mind is something that is usually covered under “multiple ways to win” but more than that are games where the secondary way to end the game is somewhat hidden or obscured from regular gameplay. Games that end early when a certain condition hits. And the accompanying sentence is: “you didn’t see this coming, did you?”
I can think of two instances this happens:
- many years ago I won a game of Goldland by taking the long way around sneaking to the treasure while everyone else was battling it out on the rest of the “map”
- much more recently: Pax Pamir 2nd where the game ends if after a dominance check any player leads by four points and where surprising things can happen in a round that allow a player to reach this state. It also enforces a certain kind of very thematic gameplay where you try to achieve this while trying to prevent everyone else from doing so.
And lastly: In Oath, as @Benkyo mentioned and I experienced independently in one of my own games, a player may not have “winning” as their primary goal for the game. This is I think an attribute reserved for any kind of game that has an on-going state that transports into another game, be it through rpg elements, campaign style story-telling or legacy elements.