It's a cleverly worded version of the "slippery slope" argument. Here is my main problem the argument:

Allowing same-sex couples would not grant new rights to homosexuals. This is a common misinterpretation. Instead, a realization would be made that the current marriage law, essentially outlining a partnership contract between two adults, unlawfully denies the rights of individuals to enter into this contract for illegitimate reasons. A contract between multiple people (as in polygamy or polyamory) or between an adult and a child (the inevitable NAMBLA argument) would be different stories altogether.

This is the reason why the argument has to be made that same-sex marriage hurts society. Whenever equal protection is denied to a group of people a reason needs to be presented for that denial. For instance, children cannot enter into marriage contracts because they would not be making that decision on their own fully informed volition.The author has adequately (imho) rejected the argument that same-sex marriages damage traditional marriage.

Perhaps you can make an argument that polygamous marriage contracts would have a negative effect on our society (maybe based on difficulty in resolving conflicts and custody rights; or based on the negative influence of patriarchal hierarchies). But that argument is independent of the argument that same-sex couples have the right to enter into an already established partnership contract.