NC'd for this as it's outing, but this happened to my DS in his last few years of primary with three other kids - very small rural school, so one teacher for three or four year groups. Every boy in several year groups had been invited but him. I was annoyed but put it down to them and him not being particular friends.
DS has ASD,and ADD. He can be fidgety, and daydreamy, but doesn't tend to be any more disruptive than any other child. So, he's sitting daydreaming (when he really should have been working), and one of the party kids punches him in the testicles. DD (different year, same class) sees and goes ape. She tells me when they get home.
I rang the school to discuss how extremely inappropriate this was, and the teacher told me that sometimes DS can distract party kid when he moves, and that party kid notices when DS isn't doing his work and is staring out the window or something instead. Like this was some sort of valid reason.
I calmly lost it. I said that if they were a few years older, I wouldn't be phoning the school to discuss this, I'd be phoning the police and making a complaint for assault. I asked where the teacher was, and why the teacher was relying on another child to violently monitor my kid's behaviour, and that as they didn't seem to be taking my concern seriously, I had no problem at all standing outside the local shop and airing my feelings to anyone and everyone who came into it.
I then said about the birthday parties, and asked why especially in a such a small school, they didn't have an 'invite all' policy like a nearby primary. The other school policy is invite everyone, or invite 10, but invites don't come into school grounds, and the 10 are not to talk about the party afterwards.
Very long, but I guess my point is, excluding just one child is bullying, and if the kids are allowed to do that, what's to stop the bullying from escalating?
OP, I think I'd talk to the school, and see if they have a policy on birthday parties, and the parents in case it was just an oversight.