Super-legislative refers to Alito's contention that the court is effectively legislating, i.e. creating new laws; and doing so by overriding the formal legislative bodies. It is implied by a belief that no existing laws or precedents recognize a right to marry.
One common criticism of courts exercising legislative powers is that they are not constrained in the same way that formal legislatures are, such as through elections.
One criticism of super-legislative powers is that they prevent future legislatures from any variation. As a (contrived) example, because of the specific ruling you mention, no future U.S. legislature can uphold a law prohibiting some same-sex couples from marrying, say those that don't plan on raising children together.
The source of the United States Supreme Court's 'super' powers is based in the longstanding idea that it possesses the power of judicial review, by which the court can invalidate the laws of legislatures (or the actions of the executive branch).
Interestingly, "super-legislative" as a phrase seems to have peaked in popularity, according to Google Ngram Viewer, in the 1930s and 1970s.
An example from the Ocala Star-Banner article "'Super' Legislative Body", published on June 18th 1964:
The Warren Court has gone off making its own laws again, usurping the legislative processes of this country.