Still circular; you (substitute "you" for the argument, if you do not agree with it personally but are advancing it as a reasonable example of a position) define marriage in such a way to exclude gay marriage, and then you use that definition to demonstrate that marriage excludes gay people. Yes, if the definition of marriage is that you need a man and a woman, then it follows that the definition of marriage requires a man and a woman.
It's still circular if you make the circle a little bigger and say marriage is defined as requiring two opposite types of people, where we define type as gender, thus it follows that that definition of marriage excludes same-sex couples.
No matter how many levels of indirection you but on the definition, if you have a definition that's crafted such that all straight couples are eligible and no gay couples are eligible, and you use that definition to prove that gay couples are not eligible, you are making a circular argument.
If you want to own the immutable definition question-begging, just go with "God made marriage this way", which is what the people not dressing up their feelings in sophistry do, and the rest of us can feel free to roll our eyes and move along.