Is it causation? It doesn't claim to be.
But, the statistical evidence shows that over the last five years (2003 v. 2008) divorce rates have fallen in states that have not banned gay marriage by an average of about 7% and fallen even faster (about 21%) in the one state (Massachusetts) that has legalized gay marriage, while divorce rates have increased in states that have banned gay marriage (by about 1%).
This result shows that the kind of evidence you'd like to see to show that gay marriage bans preserve traditional marriage, as their supporters often claim that they will, doesn't exist. The study did not count allowing civil unions as permitting gay marriage, which suggests that symbolic attitudes toward gay marriage, rather than the substance associated with marriage like legal rights for gay couples, is the important factor in the divorce rate.
Colorado bans gay marriage, and its divorce rate has been the third fastest growing in the nation. Colorado's divorce rate is up 13% in 2008 from 2003 levels. The state with the fastest growing divorce rate is Alaska.
The analysis measured divorces per marriage, rather than divorces per population, as some divorce rate statistics do.