Montresor means that he broke off the neck of a wine bottle because he apparently did not have a corkscrew with which to open it. Fortunato drank straight from the bottle. This is a dangerous way to drink wine, because breaking off the neck of the bottle leaves jagged edges of glass all the way around the rim of the lower part of the bottle. Some pieces of broken glass might even drop into the wine and get swallowed. It would seem that Montresor's wine cellar does not contain glasses, cups or corkscrews. If he had any glasses down there he could have drawn wine straight out of one of the many barrels. That is what is usually done in wineries when people are sampling wines or when the vintner is checking on the process of aging. A bit later Montresor breaks the neck off another bottle of wine:
I broke and reached him a flagon of De Grave. He emptied it at a breath.
A flagon can be a large bottle. Fortunato might have chug-a-lugged more than a quart of De Grave.
Poe may not have known a great deal about wines and wine cellars. He may not have known anything about Amontillado but chose it for Montresor's entrapment scheme for a number of reasons. For one thing, the fictitious Amontillado would have had to come in by ship from a foreign country. Since Montresor is French, he could hardly claim that he needed help judging a French wine. It could not have been Italian wine because both men would be thoroughly familiar with the Italian vintages. Montresor actually says (or writes):
I was skilful in the Italian vintages myself, and bought largely whenever I could.
The only remaining country was Spain, and Amontillado was known to be the best Spanish wine. It is therefore plausible that Montresor might have bought a pipe (126 gallons) of Amontillado because it was a bargain but that he was not competent to judge its quality and needed the help of either Fortunato or Luchesi. It is noteworthy that Montresor and Fortunato do not discuss the Amontillado at all from the time they meet on the streets until they are deep within the catacombs. Montresor wants to avoid the subject because Fortunato, if he is a connoisseur, could ask some awkward questions which neither Montresor nor his creator Edgar Allan Poe would know how to answer.