That is a stupid remark, that doesn't even make sense.
The libertarians created that straw dog out of thin air to create a distraction to use among gay marriage opponents.
Either gay marriage is legal, or it is illegal, if you don't care about complying with the law yourself, then don't, you can call whatever you want to "marriage" for yourself.
Government initially got into the marriage business because it generated license fees, blood testing fees and the like. Most of this came about in the later part of the 19th century.
Before that, it was churches which recorded marriages and the government simply recognized them.
It may not work that way now with all the faux churches performing faux marriages, but it couldn't possibly work any worse than the road we're heading down.
What these “get-the-government-out-of-the-’marriage-business’” people actually mean is that they want the government IN the civil union business. In other words, find the lowest common denominator relationship designation to apply to everyone, including blood relatives and multiples. Effectively, they want everyone effectively “married” through a back door.
If you press them hard enough they will admit this. They WANT the abolition of marriage.