MTG Arena - there's a regular play queue and a ranked queue, and people definitely play to mess around and try new decks for fun. This of course doesn't cease to induce salt from sweaty gamers in the play queue.

Even ignoring games that you consider "in the gray area," who are you to say someone can't find a way to have fun in a game that doesn't align with your way of having fun? Not everyone is playing the game hoping to land on an esports team.

Edit: I'm mostly referring to casual queues - ranked queues being hyper competitive does make sense. I've just seen the same argument made that casual queues should be the same level of competitive.

Smash Bros? Plenty of people play it as a competitive fighting game while others just like to goof around with their friends.

I said something similar in another reply, but I can't think of any games where winning/losing is possible but doesn't change my enjoyment. Even elden ring invasions feel better if you win the encounter.

The only thing that could come close is an encounter like that or in something like DMZ where you can talk it out and join forces, but maybe that's just another form of winning.

Co-op games that let you troll your buddy?

Things like L4D's primary mode and Portal 2's co-op mode.