Not directly, of course.
But their new contention is that Republican appointee, Judge Vaughn Walker's relationship status may have biased his judgement. As widely believed at the trial, Judge Walker is a gay man. Not that there's anything wrong with that -- at least according to "Protect Marriage"
Lawyers for Protect Marriage, the coalition of religious and conservative groups that sponsored Proposition 8, however, have not previously raised his sexual orientation as a legal issue.
It seems that, well...
The issue is not that Walker is gay, but that his relationship status made him too similar to the same-sex couples who sued for the right to marry, (general counsel Andy) Pugno said.
So, they think that Judge Walker could have benefitted indirectly from his own judgment, clearing the way for gay marriage.
"Only if Chief Judge Walker had unequivocally disavowed any interest in marrying his partner could the parties and the public be confident that he did not have a direct personal interest in the outcome of the case,"
Emphasis mine. Because the word "interest" is telling. It implies that that marriage isn't some religious ideal, but that it actually has tangible, mundane benefits. They are effectively admitting that this isn't about religious beliefs or tradition, but it is about denying economic and other benefits from a class of people. Benefits that Judge Walker have access to were marriage equality to become reality.
Since all heterosexual people also have an "interest in marrying", the conflicts of interest are clearly much greater on the anti-equality side. After all, since they somehow believe their marriages would suffer if they were not "protected", they have in interest in denying their benefts to them.
Just pointing out the obvious. . .in their own words.