He's silent (e.g. typically evasive and calculating) on the role of states in the link you provide. He merely says that churches and non-governmental organizations should not be banned (they aren't banned now) from performing marriage ceremonies. Here's what he said:
Gay marriage: Paul is opposed to same sex marriage, though he does not believe the federal government should outlaw same sex marriage if churches or other non-governmental institutions want to allow it.
My own position is the Ron Paul position that the state should get out of it entirely....but that is NOT the Rand Paul position at least if his speech is any indication. You may not care about the issue but to be perceived these days as evangelical apologist for the status quo is a political non-starter.