Does a game exist where some win, some lose, and some don't?
Yes. Though it's rare, some games mix up what it means to win and to lose, because why not? Games typically treat everyone as either 100% winner or 100% loser, but it doesn't have to be that way.

In real life, there are many situations where you don't just win or lose, and a lot of people are satisfied if they're able to maintain their situation. Some games mimic this.

For example, in Galaxy Trucker, rules are set out based on the story of the game. Since you're a simple trucker trying to make a living, you're a winner if you've made any money at all that game (though, as in real life, some people win more than others). If you're in debt then you've made a loss from the venture, so you're a loser. If you're on exactly 0 then you've managed to keep flying without winning or losing!

A friend of mine has a game they're making with several different endings:


If the players can't keep the game's from reaching a lose condition, everyone loses.
If the players do too well then the problem goes away without the higher ups noticing, so nobody loses but nobody wins.
If the players hold off the lose condition for long enough, the higher ups notice and reward the best player. This player wins, but nobody loses!


While some people may play with the main goal of simple victory, it can be quite refreshing when your victory, loss or otherwise is more interesting than just numerical competitiveness.