Do you know the whole class participates bc you have seen it many times or bc your DD says so? Any chance she means the "popular" girls play this game and she is not really friends with them so it doesn't go well when she tries to crash the game?
You didn't mention what her friends are doing on the playground? Start organizing one on one play dates with her friends to strengthen those relationships.
It's possible the kids are teasing her about being bad at the game and they are teasing everyone else as well. It can be hard for some kids not to see that and also interpret every remark as hostile and mean. My own DD would dwell on comments some from kids which she heard as "mean" and I had to keep reminding her that the person who said was not wasting any time thinking about that comment or her and had totally forgot about it. She believed that the person was always constantly thinking bad thoughts about her which is just not true.
If your DD is adamant that you should not speak to a teacher or counselor, you might need to consider that the situation is already at the level of bullying and she is afraid.
