You can have your views about what constitutes free speech, but the fact that US constitution is interpreted as considering hate speech to be free speech is irrelevant to your response to OP, as NZ is not under the jurisdiction of the US. The video does break NZ laws, and the steps that have been taken to prevent its dissemination follow from that. Also, war documentaries generally contain footage of conflicts which have a basis in law, while disseminating ISIS beheadings may be illegal (but IANAL).

As others have pointed out, most countries allow for exceptions to free speech in cases constituting hate speech - the fact that the US does not is a neutral fact, and an appeal to free speech absolutism doesn’t really constitute an argument for why other countries should uphold the same standards of free speech.

On Australia: we have a different political system here to the US, which is similar to NZ. While our governments are different to the UK in that parliament has enumerated powers, we don’t require fundamental rights to be explicitly defined in the constitution. The provision for freedom of political speech for instance was built up when it became apparent that the way in which we want our society to operate requires such an interpretation of our constitution. On the other hand, the US system requires a constitutional amendment for issues relating to constitutional law and fundamental rights outlined in the constitution. Both systems have their merits and demerits, but the fact that ours doesn’t work in the way that the US’s does isn’t an argument against it.

Most countries with a bill of rights, including Canada and presumably NZ, have a "notwithstanding clause" that allows the government broad power to abrogate those rights if it feels it is in the public interest to do so.

The USA is the sole major exception.

Good point. I agree with you.