I think that the argument which makes 'marriage' about the definition of the word, and not about the law's effect is clever, but misleading. When Mormons engaged in polygamy they called it marriage. It has always been about a kind of relationship more than about who the parties are. We have "going out with each other," "seeing someone," "going steady." "living together," "being a couple," etc. - all are descriptions of a kind of relationship. The wider subject is romantic relationships, the descriptors have a connotation of a level of psychological commitment, they separate one kind of romantic relationship from another. But, I think that the whole 'definition of marriage' argument is a rabbit hole. The real issue is about a 'license.'
When a government issues a license we tend to think of it as granting permission. But that is also a kind of misdirection. What actually happens is that government sets conditions which prohibt anyone, except those who meet whatever conditions they establish, from engaging in the licensed actions. A county in Lousianna might pass a law which states that no one can rent out a room in their house without becoming a licensed 'Hotelier' or something like that. There are jurisdictions where no one can accept money for braiding hair without becoming a licensed beautician. With marriage, no one can get married without meeting whatever conditions have been established by the jurisdiction. Some governments made themselves the 'definers' of the word marriage. They might say you have to pay a fee, get a blood test, be of a certain age, live in the jurisdiction, be of the same race, swear an oath, be an opposite sex couple, etc. Every single condition is a restriction enforced by law.
Licensing is always a form of prohibiting by threat of physical force.
And it isn't the government who should be enforcing anyone's idea of what the proper definition of the word 'marriage' is. As a Devil's advocate, one might say, "Even if marriage is properly, logically, and once and for all, defined as ONLY between one man and one woman, it still would not be the place of the government to stop people from going through some kind of ceremony of their choosing, and then mistakenly calling themselves married if they aren't an opposite sex couple." But that isn't what I believe regarding the definition. I believe that when properly defined marriage might include more than two people and the people could be opposite or same sex and that the relationship is romantic in nature, and that the marriage is a personal commitment that may be shared with friends and family.
Marriage does has civil law ramifications: inheritance, childcare responsibilites, divorce, property distribution, power of attorney, etc. But all of those can be handled with simple contracts. Who hops over a broom with whomever is not for the government to decide.
Here are the possible ways the Supreme Court could have gone:
1. Marriage is only between a man and a woman and no state or local jurisdiction shall act otherwise.
This is what the hard-core religious right would desire - imposing a religious view on all. But many, who are not religious at all, are uncomfortable with the cultural changes we see where old institutions and traditions, which bind our culture together, are being turned upside down and if that feels personal, they too might take this position.
2. This is an issue that must be decided on a state by state basis.
This position is less adamant, not as strong, and represents the conservative's drive to observe states' right.
3. Gay and lesbian couples have the same rights as opposite sex couples and all states must issue them marriage licenses.
This is the progressives drive to use Cultural Marxism and Identity Politics to pursue their goal of transforming the nation. It is also the position of those who don't want to see gay and lesbian couples denied equal rights, and buy into the idea that it is okay for government to be in charge of who should get married.
4. Getting married, whoever that might or might not include, is not something a government has a moral or legal right to interfer with.
This is the position that Objectivists should hold - where government's purpose is derived solely from the protection of indiviual rights.