It's a very strong claim that gay marriage opponents are making here. If being of two different genders is an essential part of the meaning of marriage, then "gay marriage" is like "round square" -- something logically impossible and unimaginable. I hold that "gay marriage" is more like "flying pig" or to use David Lewis' example, "talking donkey." We can imagine these things, even if the latter term ("pig", "donkey") would usually predispose to expect that the former term ("flying", "talking") won't be present. I can easily imagine two people of the same gender getting married. (By the way, I wouldn't bet against the ability of biologists a thousand years in the future to generate actual flying pigs and talking donkeys.)
Let me list some other things that contribute to something's being a marriage. None of these are necessary or sufficient conditions, but they do contribute to something's being a marriage:
-Being, or having been, in love.
-A commitment to having sex with only your spouse for the rest of your life.
-There being a big ceremony intended to initiate and celebrate this commitment.
-Living together, or wishing you could if circumstances prevent it.
-Having sex with your spouse, or having done so on a regular basis.
-Raising children together (which gay people can do, given adoption or artificial insemination).
-The application of some legal stuff to you (about the inheritance of property, health benefits, taxation, recognition of what you're doing as "marriage", etc.)
-Some externalist elements -- whatever marriage is, it's what my mom and dad and various other couples I know are involved in.
To see how flexible the concept of marriage is, consider this ancient Chinese folk tale about the origins of silk, which involves the possibility of inter-species (though heterosexual) marriage:
Legend has it that once there lived a father with his daughter, they had a magic horse, which could not only fly in the sky but also understand human language. One day, the father went out on business and did not come back for quite some time. The daughter made him a promise: If the horse could find her father, she would marry him. Finally her father came back with the horse, but he was shocked at his daughter's promise.
Unwilling to let his daughter marry a horse, he killed the innocent horse. And then a miracle happened! The horse's skin carried the girl flying away. They flew and flew, at last, they stopped on a tree, and the moment the girl touched the tree, she turned into a silkworm. Everyday, she spit long and thin silks. The silks just represented her feeling of missing him.