For our purposes, let's boil it down to the short-term explanation and the long-term explanation. The short-term explanation is very clear. It's the recession, which has delayed every hallmark of young adulthood -- getting a job, moving out, getting married, having kids, and so on.
But this delay is part of a longer delay of marriage that stretches back about half a century. As more women attended college and worked through their 20s, they built enough financial independence to wait for marriage. Meanwhile, the cost of being single fell dramatically, as birth control technology extended courtships, home tech (e.g. washing/drying machines, video games) made it easier to live alone, happily and cleanly. As you can see in this study by Betsey Stevenson and Justin Wolfers, marriages per capita have been declining since the 1940 (except for a little boomer-fueled uptick in the late-1960s):
Out-of-wedlock births and delayed marriage were already underway before the 1990s, when gay acceptance took off. This suggests that gay marriage isn't leading to the decline of marriage. Rather, the "decline" of marriage happened to pique media interest at the same time that homophobia got smoked -- in entertainment, in federal law, and in wedding chapels.
The old conservative argument against gay marriage was that it would ruin the institution for straights. But Douthat's argument -- that gay marriage reinforces the idea that marriage and childbirth don't have to be connected -- acknowledges the exact opposite. It accepts that straight marriage "ruined" itself in a way that gay marriage won't fix. That's not a reason to oppose gay marriage. It's just an acknowledgement that gay marriage won't change anything for straight couples.
And wasn't that the point, all along?