Let me just focus on the issue of marriage licenses. The article you referred to stated,
Yes, couples could make explicit contracts and have divorce conducted through private arbitration. But what if it's something other than divorce? Suppose a couple enters into a marriage contract but neglects to specify where their respective property goes if one of them dies? You may think this is highly unlikely, but you'd be surprised at how many people die without a will (many don't want to think about their own mortality, so they keep putting off writing a will).
So we have a situation where someone's dead and there are various claimants to his or her property. In your ideal anarchic society, how is the ownership of the property to be determined? It's no answer to say that the couple could or should have included testamentary provisions in their contract -- the fact is, they didn't. So who gets the property?
In the real world every state has intestacy laws that provide who takes the property -- usually the surviving spouse and children. But presumably you don't want government to be involved in such things. So who decides what happens to the property? Do the claimants battle it out in an Iron Cage Match (think 50's and 60's TV wrestling)?*
What I'm suggesting is that in certain circumstances it will be necessary for some rule to be applied by the government to determine such matters, and if the rule is going to say that the "surviving spouse" gets the property it'll be necessary to have some way of determining just who that is. If your answer is that the couple can simply file a copy of their contract with the government, how does that really differ from a marriage license? In other words, if the government will recognize someone as a "spouse" only if a copy of a contract is filed, is this any different than saying that the government will recognize someone as a "spouse" only if a marriage license has been issued?
* In all seriousness, in a purely anarchic society who gets an intestate's property?