We were playing. So a girl got eliminated.(out). What's a more natural to say that?
Why did you out me?
I mean doesn't "eliminate" sounds a bit formal. I know "out me" sounds unnatural. What would you use?
In British English there is the word knockout, see the Oxford Dictionary.
A tournament in which the loser in each round is eliminated.
So it isn't just used in a boxing match, when the opponent is floored. One example given is:
They qualify from their group but fall to Argentina in the first round of knockout matches after a penalty shoot-out.
So you could say
The girl was knocked out of the game.
The girl could ask
Why was I knocked out of the game?
I agree with @WeatherVane that you want "knocked out" if you want something that sounds more casual.
However, I will note that "out me" does not sound unnatural, it just means something completely different. The be 'outed' means to have something you were keeping secret revealed. This is by contrast with "coming out" for voluntarily revealing something you were keeping secret. Most often, in my experience, it's used about sexual orientation and gender identity stuff ("coming out as gay"). If you don't qualify it usually means something of that sort, but one can also "come out as a liberal" to one's conservative family, for example.
She’s out! is the normal expression. It’s actually pretty ubiquitous, since it’s used in many different sports and even some video games.
Dodgeball? You know the rules and maybe you saw the movie starring Vince Vaughn and Ben Stiller in 2004. But the concept is pretty simple — throw the ball at your opponent and if you hit him or her, they're out of the match.
Missing the ball this way is called a “strike” and in baseball three strikes means you are out!
On its face, "HQ Trivia" is a simple, multiple-choice trivia game. You watch a host as he/she rattles off question after question - if you get the answer right, you get to keep playing. Miss one, and you're out.