Yes it does, under Article III, Section 2:
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution......--to Controversies between two or more States; between a State and Citizens of another State; -- between Citizens of different States......, and between a State, or the Citizens thereof, and foreign States, Citizens, or Subjects.
Also, Article IV, Section 4:
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against invasion....
Also, Article VI, the Supremacy Clause:
This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding.
(Emphases added.)
The Massachusetts supreme court has, in an egregiously abusive ruling en banc, handed down a novel law, written in a Star Chamber, that has no precedent whatsoever in United States or English law, that has not been deliberated by any legislature in the Union, granting pretended rights to a small, litigious, and factious constituency that have not been agreed to, and are indeed opposed, by the People of Massachusetts and by the Peoples of the rest of the United States of America.
This egregious and usurpatory enactment of the Massachusetts supreme court stands in violation of Article IV and its guarantee of a republican form of government, for which these four judges have substituted oligarchic rule by decree.
Furthermore, the United States Supreme Court having ruled many times on matters involving the institution of matrimony, the Massachusetts supreme court would appear to be likewise in violation of Article VI, amending by decree a legal institution of settled definition in a rebellious and insurrectionary manner, which decree pretends, by the operation of the Full Faith and Credit Clause, to alter and amend in a peremptory manner both United States Supreme Court rulings and the laws and constitutions of the other States of the Union.
The controversies among the States and the State of Massachusetts thus generated are justiciable under Article III of the Constitution, quoted in relevant part above.
You have asserted, and I have refuted, your claim that there is no authority for the United States Courts to intervene.