Lyle Denniston attempts to answer the question:
With the demise of the Defense of Marriage Act’s benefits ban in Section 3, for legally married gays and lesbians, the Court immediately — even if inadvertently — gave rise to a situation in which couples living in states that will not allow them to marry because they are homosexuals will still be able to qualify for federal benefits, many of which are handed out or managed by state governments.
But the ruling did not do anything explicitly about another section of DOMA — Section 2, which gives the states the right to refuse to recognize gay marriages performed in other states. That thus raised the prospect that a same-sex couple married in one of the states now allowing such unions could face obstacles to their marital rights when they moved into states that still do not recognize their unions. This might be a particular problem for already-married gay couples serving in the military, who often have to move from state to state.
Ilya Somin examines the situation in California:
As Marty Lederman explained in this January post, it is not entirely clear whether Judge Walker’s district court opinion striking down Proposition 8 is binding with respect to gay marriages other than those of the plaintiffs in the case. As Lederman points out, both sides in the litigation agree that he intended it to be so binding. But they differ on whether he had the power to do so. The Supreme Court’s opinion in Hollingsworth does not address this question, which could end up being settled by lower court litigation. Lederman also notes that the governor (who opposes Prop 8 and refused to defend it in court) could simply choose not to enforce Proposition 8 in the aftermath of the Supreme Court’s ruling. In practice, therefore, it is quite likely that Proposition 8 will no longer be enforced even if Judge Walker’s ruling isn’t binding beyond the parties to the immediate case.
In a press release California Governor Jerry Brown writes that he has “directed the California Department of Public Health to advise the state’s counties that they must begin issuing marriage licenses to same-sex couples in California as soon as the Ninth Circuit confirms the stay is lifted.”
(Map of states with full marriage equality from The New Yorker)