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Seems that way:

U.S. Constitution

Article. IV.

Section. 1.

Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.

Section. 2.

The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.

Just a few observations.
My understanding of the DOMA case was that the provision that gave states protection from having to recognize gay “marriages” from out of state was not challenged or considered.
So that part of DOMA remains intact.
That explains why thus judge went the 14th Amendment rout. That’s a tough position on appeal however.
The premise of his ruling is that gay marriage is a fundamental right, and cannot be summarily taken away by another state.
Number one, it is not established law that gay marriage is a fundamental right.
Number two, he addresses this fundamental right issue without the need to do so under a 14th Amendment analysis.
If the law has historically allowed all married couples, including married cousins (who are not allowed to marry under Ohio law) from other states to be mentioned as husband and wife on death certificates, then the unequal treatment treatment is the best argument for an equal protection violation.
But he misses the point entirely. The state of Ohio has treated all out of state heterosexual marriages the same pursuant to state law.
It is well within the realm of state authority to decide which out of state marriages not otherwise permitted under Ohio law, may be recognized. There are ample legitimate basis for such a determination that gay “marriage” has no historical legitimacy in this country, and that the fundamental nature of same sex unions is so far off the mark that is doesn’t deserve the same treatment.
Reasonable people cam disagree about marriage to first or second cousins, and there is plenty of historical support for such marriages. The beginning of civilization with Adam and Eve was followed up by marriage between siblings, cousins, etc. it was necessary, and God did not call it an abomination.
The same Old Testamemt did however state the wickedness of homosexuality.
So my point is that Ohio has a legitimate basis for its position here, and frankly I think the 10th Amendment carried the day in favor of Ohio.