Here's the text of the 14th amendment:

No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws

I bolded the last clause for emphasis.

Now, what is a marriage? It is a legal contract between two people who have the legal right to enter into legal contracts. It is nothing more and nothing less than a legal contract that conveys specific legal rights and responsibilities to the parties that enter into it. Under the 14th amendment, no state has the right to deny people the equal protection of the law. Therefore, states cannot define marriage as limited to two people of different genders. Any "originalist" who says, as Scalia has said, that "words have meaning," can clearly see that the constitution does not specifically limit marriage two a union between a man and a woman, so therefore, if the two parties in the contract are two people, then they are to be afforded equal protection under the law. Any true "originalist" would have interpreted this amendment to mean that gay marriage is absolutely and without question legal under the auspices of the 14th amendment.

Scalia was a partisan hack with a great gift for articulation. The fact that he could create a good argument, and that a lot of people who liked him also liked to wrap themselves in the spectre of a document they've never read or bothered to try to understand doesn't make him any less of a partisan hack. He was a partisan hack, plain and simple.