"Delicatessen," in this case, denotes the older sense of food for sale, not the store from which food is sold. Another example — "we have a fresh stock of choice groceries and delicatessen" — appeared in an advertisement by the Houston grocer R.T. Andrews for Eastertide 1924. If the name of the business that commissioned the sign shown here once appeared along the roofline, it seems to have been effaced during recent repairs.
Choice groceries and delicatessen
Surviving (but probably partial) signage, 989 Home St. (at Vyse Ave.), Foxhurst, Bronx
Now the site of El Fogon Center for the Arts