He’s only dancing the Salsa that Americans will no longer dance. If he was in the country illegally when they performed the farce then he is not legally married.
As a matter of law, it's a bit more complicated and your statement is not entirely accurate.
First, there are two sovereigns we're talking about - state & feds. I'm not familiar with any state law that prohibits the recognition or allowance of illegal alien marriages. Most states (perhaps all states), just as a matter of law, don't make either of the couples' citizenship or immigration status a condition of marriage.
For the purposes of federal immigration law - if you want the feds to recognize your marriage in order to obtain a green card for one of the spouses, then that spouse must be able to unequivocally demonstrate that they entered the country legally, but it's not necessary for them to currently be in the country legally, per the Immigration and Nationality Act. IOW, a person could have overstayed their visa, gotten married and still have that marriage count for the purposes of obtaining a green card.
Having said all that, this story has absolutely nothing to do with immigration law, and everything to do with DOMA and homosexual marriage. Holder wants another prong of attack against DOMA's prohibition of recognizing homosexual marriage for the purposes of immigration law.