It is entirely correct... the website actually confirms it... it is entirely a regulatory function of legislative declaration and it is confirmed by court decree in cases where property and child custody are issues...
Then perhaps you missed this section of the link:
While the various state courts have prattled on for almost 200 years about what the laws of their states do and do not allow concerning marriage, the US Supreme Court cut straight to the heart of the issue in declaring that statutes controlling marriage can only be directory because marriage is a common right, which is not subject to interference or regulation by government. Or phrased another way, the God-given right to marry existed prior to the creation of the states or the national government, and therefore it is beyond their purview to alter, modify, abolish, or interfere with, such a right.
In its decision in Meister, the Court refused to even examine the numerous state court decisions prior to making its own decision. While this was assailed by legal commentators of the day as an egregious choice, we can only agree with the Court in its choice because a state court opinion has no authority to affect a fundamental right that existed antecedent to the formation of the state.
It should be noted that Meister has never been reversed and is still controlling case law concerning the fundamental right to marry without state interference.