As I understand it, the argument goes that if State Y has to recognize State X's marriage license, because of section 1 of the 14th amendment, then that same precedent also applies to State X's conceal carry licenses and State Y has to recognize it as well.
But this decision was presented by the court as a corollary to the Fourteenth Amendment right to marry:
As counsel for the respondents acknowledged at argument, if States are required by the Constitution to issue marriage licenses to same-sex couples, the justifications for refusing to recognize those marriages performed elsewhere are undermined. See Tr. of Oral Arg. on Question 2, p. 44. The Court, in this decision, holds same-sex couples may exercise the fundamental right to marry in all States. It follows that the Court also must holdand it now does holdthat there is no lawful basis for a State to refuse to recognize a lawful same-sex marriage performed in another State on the ground of its same-sex character.
So for the same argument to apply to (for example) concealed-carry licenses, you would first need (for example) a ruling that any state must issue a concealed-carry license to anyone who wants one.
At that point, it would become possible to point to the precedent of Obergefell v. Hodges and say that in that case the states must recognize each others' concealed-carry licenses.
Edited by Dr Adequate, : No reason given.