Yes, they do have First Amendment rights, just not to the same degree as adults. This is the same as other rights ā they can't buy guns, vote, etc. either. The point is that it's definitely not a slam dunk case as claimed. I'd love to hear a constitutional lawyer weigh in, if there are any here. I used to be a lawyer, but this was never my specialty.
If someone could extralegally ground me with no devices if I say something they don't like (provided that it's speech protected under the First Amendment -- since not all speech is), I essentially have no First Amendment right.