These cards are blank on the back, so aren’t meant to be used postally. But they are the same dimensions as a standard postcard.
The Texas Zephyr tells passengers they can find the diner “just ahead of the Pullman while a “buffet-observation lounge is provided at the rear.” Unmentioned is the dinette car for coach passengers. Since the lounge-observation car at the end of the train was not open to coach passengers, it seems likely this card was given solely to Pullman passengers.
The California Zephyr card stresses the reservation system for dinner in the diner. Strangely, many trains did not have a reservation system, leading people to stand in the corridor next to the kitchen waiting for a table.