Both sound fine to me, although they do represent different perspectives on being "out" of the game. In a game like Monopoly, one doesn't just "go" out -- one is "kicked" (or "sent") out by the player who takes all your money. However, when the girl says
I got out of the game.
it implies that she did so more or less voluntarily. It's not incorrect English, but it does suggest she views the circumstances differently. Meanwhile
I was out
is somewhat more ambiguous. It describes the situation, but does not imply whether the reason was voluntary or involuntary.
Consider the following three examples:
Amanda: Do you still work for that company that you said you hated?
- No, I got out of there months ago (I quit)
- No, I was kicked out of there months ago (I was terminated)
- No, I was out of there months ago (ambiguous)
Side note: The use of "like" in "like two hours ago" is colloquial, and common in my local dialect (Southern California / US). I can't say how common it is elsewhere, but I try not to say it too often when I travel to other parts of the world.