Commitment or covenant, aka promise, need not be a written thing. You can look a woman in the eye and tell her you’re taking her as a wife, and if she doesn’t cry rape, and you consummate the relationship. I say you’re married. You sealed the deal.
The only differentiation in scripture that I can find between instances of whoring, and other elicit sexual acts between available couples and marriage is a choice/covenant/commitment to be married. Or arguably the payment of a price, which in my mind is the same as making that commitment.