I seem to recall that you could find this sort of card as a handout in the lobby of theaters for the most premiere class of roadshow releases. I used to have one for How the West Was Won, although it has been lost for years.
I think it was mostly for Cinerama releases. They were trying to build buzz, so mailing a postcard from the lobby bragging you had seen the film was a promotion they tried. Yes, I believe you could get a stamp there as well. I remember the little cardboard "mailboxes"