Marriage in some countries comes with a bunch of legal rights and obligations, so you do need the government to agree if you also want it to enforce those things.

In New Zealand, marriage has no legal value as far as I know. All the law that I know of, such as for property rights, immigration, and social welfare that would usually be about marriage is instead about being in a "relationship of the nature of marriage". That's kind of scary because you can sleepwalk into becoming effectively married and then suddenly you lose some of your property rights.