That is what a marriage (in the United States) is. It is a civil contract. There is nothing inherently religious about it. You can go down to the county courthouse, pay $20 or so, and be married by a judge.

That some religions have a "marriage" ceremony is orthogonal. What makes you married in the legal sense is the marriage certificate you get from the government. Any ceremony is just for show. What the US Government defines as marriage is purely a civil thing.