I know it hurts. I am a mother also. I have also been on the “neb” list as a young child at times, so I understand about being left out and not being included. It hurts, but it probablly hurts the mothers more.
I think you should not make an issue out of it because this is the way it is. You and I know that Hashem has sent this to him, and we as adults may be able understand that not all kids are socially invited, but he, may be better able to actually brush it off practically, and go on with life and what other things he could do at recess besides feeling sorry or angry at “the way it is”.
As a mother your job, and influence should and can be to show him, (indirectly) just how to move on, and accept things.
So he doesnt get to play the games at recess. Its not so terrible.
Let the kids work it out themselves. If you get involved it can make things worse sometimes. It can make the boy feel weak and more vulnerable when he sees your emotions as per how you’re handling it and being upset for him.
You’re not “Stuck” as you wrote above, this is his lot, for now.
Your job is to help him deal with it positively and perhaps this is Hashem’s blessing and opportunity for him to stick around the other kinds of boys who are also not playing, and what I have found in life, is that each “missed opportunity” was in fact a blessing in disguise. Maybe the boys not playing games are in fact smarter or more studious, and destined to be learners.