Inspired by the reverse question.
My wife and I play a lot of board games (e.g. 7 Wonders, Carcassonne, Ticket to Ride), and some card games (e.g. gin rummy) or video games (e.g. Mario Kart). We both quite enjoy them, though they’re more important to me than she.
For the most part, she refuses to play competitively: she’ll play as well as she’s able, but only up to the limit of what she can do without messing up others. This does not interfere with her enjoyment of the game! She’s happy to play without any serious regard for winning or losing, and is much happier not being competitive.
This seems to be guilt-driven: she feels bad ruining anyone else’s strategy. For examples,
In gin, she will be (a little) upset to learn that she had a card another player needed to win, even if she 1. also needed it, and 2. had no way of knowing that in the first place (neither of us is much good at counting cards, and in particular she makes no attempt to do so).
She’s very careful with shells in Mario Kart, to make sure she only ever uses them on computer opponents rather than one of the human players. She’ll let a blue shell (which automatically attacks the racer in 1st place) sit unused, blocking her ability to pick up something else, if she knows I’m in 1st. If she accidentally does hit me with a shell, she feels some (moderate) guilt about that.
Neither of these things necessarily ruins the game for her, and she’s certainly not distraught or anything about it, but the negative feelings associated with these things are enough to affect how she chooses to play the game, as evinced by the blue shell thing. She isn’t particularly bothered by this, and enjoys the game even if she loses. She’s certainly much happier losing than she is with the negative feelings associated with attacking another player. As such, she has little motivation to change, and therefore change may be impossible and attempting to change her might well be inappropriate. I know that.
On the other hand, I think she might enjoy the game more if she got a little more competitive. Certainly I don’t think she ought to be experiencing negative emotions over playing a game well and fairly; alleviating those would be a primary goal.
And yes, to be honest, it affects my experience as well: I end up trying to play “nice” both out of a desire to reciprocate and also to try to keep the playing field level, but ultimately there is zero way to know if I won because of better play, or because she “out-niced” me. It would be nice to be able to convince her that I would enjoy the game more if she frustrated my tactics, than if she let me win. I have said as much, but she doesn’t seem to buy it—or, at least, doesn’t buy it enough to feel free to do so and not feel guilty about it. It feels a little silly that her attempts to improve my play experience actually degrade that experience.
The goal here is not to enjoy game time with my wife: I already do that. Therefore, answers focusing on playing something else, like a cooperative game (Pandemic is already one of our favorites) are missing the point and not answering the question. The goal here is also not to enjoy the challenge of stiff competition for its own sake: I already do that, too. Therefore, answers focusing on finding that challenge elsewhere are also missing the point and not answering the question.
The goal here is to alleviate her negative feelings associated with competitive play, hoping to achieve greater satisfaction and enjoyment of game time for both of us. Answers should focus on how to achieve that, if possible, and if an answer wishes to claim it is not possible, which may well be true, that needs evidence to support it. Answers will absolutely be judged on how well they Back It Up! per Stack Exchange principles, and answers that assert facts without backing them up will be downvoted.