The essential public purpose of marriage is to attach mothers and fathers to their children and to one another.
Rob Tish takes a moment to pull it apart. NOM, of course, doesn't define the words it uses, trusting to take their implied meaning.
What is the purpose of something? Whatever we want it to be. But many people want our thinking restricted to whatever was designated by the owner or designer. So, if sex is designed by God, we must restrict ourselves to the purpose God declares for sex. (That NOM may have misinterpreted God's purpose for sex is not explored.)
On to the "public" purpose. The definition of this term by the citizenry is too varied, so that can't be it. Government's definition? That can be inferred from the Declaration of Independence. The purpose of government is to secure the rights of life, liberty, and the pursuit of happiness for the citizens. So government is to support whatever kind of marriage makes me happy.
Essential? Meaning if you didn't have some important ingredient some thing would not exist. NOM says that kids are essential to a marriage, without the little ones marriage doesn't exist.
So many lies in so few words.