i had done competing in various events, physical (martial as well as non) as well as non-physical. i usually, not always, didn't give much thought on winning or losing. i just competed. sometimes i won through skill, other time i lost through luck. maybe for you, competition is about winning or losing, but not for me. i don't know you, but believe me, i know me quite well.
The definition of compete
includes having the goal of winning. The fact that you "didn't give much thought on winning or losing" is irrelevant to the motivations of competition because you weren't competing.
But while we're on the subject of joining competitive activities without competing...
The game "Sorry" is great because you can play it to win or you can play in such a way that advances everyone else.
The object of the game is to get all your pieces onto the board, around it, and finally to a "Home" point at the end of the line before any other player. So it is a competition.
I have played the game two ways - wanting to win or wanting to use every opportunity to help my opponents!
Playing for everyone
in the game to receive the maximum benefit and least detriment from my choices in the game is one way to play. Using the game cards to advance myself to Home while trying to keep the others from succeeding is another, and the more typical way of playing.
When played for an enjoyable experience for all, using all my opportunities to advance as many of the players and working to diminish any harmful effects to others, I am not competing, am I? Even though the game is producing a winner and losers, I don't have the spirit of competition, do I? I just have interest in seeing how things turn out without trying to best anyone.
Other times I can be a cut-throat competitor sending my loved ones back to start with the callousness of a dictator.
The interesting part is that though you are forced to make choices in the game that significantly inhibit the progress of your opponents or inadvertently add to it, the random factors of the game render those effects, seemingly large at the time, to be relatively insignificant in the long run. I have never found the outcome relative to anything anyone does to anyone else in the game except in the most marginal way.
The difference in the outcome depending how the game is played can be dramatic! When people play cooperatively they appreciate the way the game decides whose game pieces all reach "Home" first. Though one may be declared the winner, everyone celebrates who had the luck of the draw.
When they play to win they feel bad losing, like if they had made other choices or not been so nice they would have won. Or if they win they can feel like they are special or smart or have superior skills that had something to do with it.
Might those spiritual effects have anything to do with a "strict prohibition" regarding competition in aikido?