He is right. The practice was quite common on the frontier from the beginning right up into the 20th Century. An example would be Wyatt Earp. He had two common law wives in his lifetime. There was no licenses or church weddings, they just lived as husband and wife. I would speculate that what we see today as common, the big church wedding was beyond the means of most in the 18th and 19th Centuries. Recently read a history of the Hatfield McCoy feud. Marriage was not done with govt. licenses or church for that matter. People just lived together and just proclaimed themselves married. As for gays(females only), they even had a name for it. When two old spinsters lived their lives together it was called a Boston Marriage in the 19th Century. They difference was that if someone did not like it, they were not forced to accept it themselves, unlike today.
He didn’t mention common law marriage, he mentioned shacking up until they could get married.
Common law marriage still exists and is recognized by the federal government and all 50 states, as long as it is a legal, common law marriage, if indeed Earp was legally common law married.
Marriage licenses have existed for many centuries, since the 1300s, and before that Banns, and before that other formal actions that made marriage legal, Thomas Jefferson obtained a marriage license.
Contrary to your claim, there was no gay marriage, there has never been a time when a couple, or a few people could not decide among themselves all kinds of things, but it didn’t exist outside of their imagination. Right now you can call whatever you want “marriage”, you could yesterday and ten and 20 years ago.