Well right off the bat, the fact they put it as "gay 'marriage'" is kinda funny to me. (Cause they're not really married you see, but this a balanced article)
But really, right here at the start it falls apart for me. "All four argued that redefining marriage to include same-sex couples would harm children by depriving them of a mother or father." Single parents exist and removing gay marriage won't magically give them other parents. Unless they plan on passing some law that parents of children MUST be married the gay marriage part has almost nothing to do with that.
I also checked for "divorce" or "single parent" in the article since these are far, FAR more likely to lead to children without the daily dose of "both sex parents" they seem to be arguing about but found zero mentions.
Therefore I will have to fall back on what others have said there. This is the children of a few fundamentalist LGBTQ parents (maybe, we don't hear from them) who didn't like their upbringing (possibly due to crappy parenting). What I don't see is any justification for removing gay marriage, unless you count "If we don't, it'll be normal and then we can't remove it".
If the argument is keeping kids in dual parent homes, there are much, much greater issues to deal with if you want to travel that road (not a lot of people do) that includes divorce, if one parent dies or some other mishap occurs, children raised by grandparents or relatives for any number of reasons, in vitro etc.
It really just seems like crappy parenting is being as an excuse to hit what they really want to hit, gay rights. You could just as easily walk over to any other group and find fringe elements but a call to remove their rights would be just as dumb.