Don’t be so sure she isn’t.
If a prominent Democrat's child is under 35 and went to Stanford and Columbia the odds are high enough that they support gay marriage that one doesn't have to assume anything further about their sexual orientation (though with politicians' kids homosexuality is always a possibility).
I'm not sure Chelsea Clinton actually did influence her father's views on this, though. Bill Clinton would have gotten there on his own, like the rest of his party.
He's probably just trying to get his daughter's name in the press to promote whatever she's going to do next. Run for office, maybe? Or just run his foundation?