I'm afraid I don't have any idea regarding the inception of the Abbott's shop (why not ask them? (www.Abbottmagic.com
As to Ton's shop, it is one of very many such brick and mortar establishments that incorporated "stages" of varying sizes. Here in the United States, many (probably most, if fact) such shops still in business are located in the less-expensive per foot real estate "strip malls."
Nearly every strip mall store has a store front (retail) area, and another back (office or storage area). In some I've seen, the back area is much larger than the part the customer sees.
These areas in the rear of the shop were and are very often converted, in part, to a small proscenium stage area.
ArsPraestigium.com - Purveyors of the ART of Illusion