Well, yes they are classical. However, someone had the idea to put both pieces on one side of a 12 inch record, which is kind of odd, since they don't have any thread to connect them that I can see.
I own the remake of this disc with orchestral accompaniment and as far as to my knowledge it seems to be just a coupling of two short pieces by the artist and or recording director at Victor to fit on one 12 inch side. They also did this with a few short instrumental pieces and at least one other operatic I am immediately familiar with which is 88441 - Don Giovanni - Deh, vieni/Damnation de Faust - Devant le maison as sung impeccably by Emilio de Gogorza.