Not according to the dictionary;
government of a state by immediate divine guidance or by officials who are regarded as divinely guided
A theocracy has priests or a priest-class as supreme rulers (as in Iran, Afghanistan). But the state’s recognition of marriages being valid if officiated by whatever religion the couples choose does not fit that pattern. Rather, it is acommodating religious people, licensing them (whatever religion) to do duties that would be the governing body’s work. Here (Norway) licensed religious officials can officiate marriages, and the government recognise them. This does not mean that Norway is a theocracy. The recognition of religious marriages does not mean those are the only options. You can also get married at a courthouse, by a judge. Or you can go abroad and get married in whatever way, as long as it is an officially recognised way.
It is a place where members of certain religions have additional formal legal rights. That isn’t a democracy in my book; it is kind of the opposite. Sure Christians get away with a lot where I live, but their advantages are not written into the laws.
Here, the biggest humanist organisation can also officiate marriages. Haven’t checked if any of the smaller ones can do it also, but there would be nothing stopping them if they wanted to. A marriage is basically a legal contract. It is up to the people getting married which variant they choose, and who they want to officiate or witness the signing of the contract, with whatever rituals they choose. They can go fully religious, or they can do it secularly through an organisation, or at a courthouse. It’s still basically just a legal contract, witnessed by whatever licensed persons of their choosing. I don’t see what this has to do with democracy or not. And I certainly cannot see anything undemocratic in it.
But of course, if you want your religion or your religious family to recognise that you are actually married, you might have to go through the extra steps of promising stuff to a sky god. But as far as official records go, it’s just some signatures on a contract conforming to certain legal formalities.
Edit: yes, they dress those contracts up with flowery language and shit. But that’s more for shits and giggles, and because people feel better about it. But they still conform to the legal requirements. Which is the important part.