그만 has another meaning too.
This 그만 is adverb.
That sentence can be understand like this.
You fell down on that stairs today. Because you run to hurry.
So 그만 is adverb for 넘어지고 말았어요.You don't have choice to fall down.
So 그만 doesn't have important meaning in this sentence. Because that 그만 is just adverb.
그만해! 늦겠다! 학교가야지!
Stop it! You will be late! You must go school!!
술을 너무 많이 마셔서 차에서 그만 자고 말았어.
I drunk a lot. I slept in the car. (I don't have choice to stop my sleeping.)