The only thing the Court says on the matter is:

>There are reasonable bases to conclude that intermediate scrutiny is appropriate even under these circumstances. We need not, however, definitively decide that question because we conclude the Act “passes muster even under the more demanding standard.”

It's possible that either Judge Ginsburg or Judge Rao think the strict scrutiny should apply, but if forced to put money on it I would say they both land on intermediate scrutiny.