Nope. Reread the case. They argue that the federal government has the obligation to recognise marriage as between a man and a woman.
They go on to argue that a state deviating from this principle would result in anarchy.
They also argue that marriage is older than the common law, and that the common law cannot change marriage.
Well first, when you say "the case", are you referring to Reynolds v. United States (circa 1870s)?
And again, I haven't read the case in a very long time, but remember what is discussed in dicta is wholly separate from the legal holding (and binding) element of the decision. Dicta can be read (or ignored) as persuasive precedent.
Marriage now: man & woman
Marriage soon: man&woman, man&man, woman&woman
Marriage coming: above plus transgender&all above, man&boys, woman&girls, man&sheep, woman&dog or snake, etc, and of course man&multiple wives, woman&multiple husbands.
Anything less would be discriminatory and of course un-Constitutional (as if there was a Senator or Congressman who would know the Constitution if it bit him/her/it on the *ss.)