Oh, brother. What a stupid argument.
One way we can see how bullshit this argument is is that they only quoted one person who believes in it. They quoted the hell out of her, too. But there's no issue here, except to people who want there to be one. Under widespread principles of statutory construction (meaning the way courts construe statutes), there is no issue here. If I were a judge hearing a case brought under this, I'd sock the plaintiffs attorneys with fines for frivolous lawsuits.
Support for same-sex marriage (or for any issue, really) is ill-served by promoting absurd arguments like this. Obviously, they're saying nothing other than actual marriage, as defined in #1, can be recognized as having the status marriage has.