A food item requires two pieces of bread in order to qualify in the category of "sandwich". This is according to the Merriam-Webster dictionary, a hot dog is one piece of bread with meat and fillings inside. The mere fact that a single piece of bread has a unique shape does not make it a sandwich. A piece of toast with toppings would not be considered a sandwich, because it is a single piece of bread. A hot dog is the same thing, just with a specially shaped piece of bread. In fact, the definition of a hot dog in the dictionary is "a frankfurter with a typically mild flavor that is heated and usually served in a long split roll" . This includes no mention of the multiple pieces of bread required for classification as a sandwich and does not even necessitate the use of bread at all as a critical part of designation as a hot dog. Thus, by nature, a hot dog would not qualify as a sandwich. Its own definition does not allow it to fall under that category and it should not be attempted to be placed there.
Although the hot dog definition may not classify it as a sandwich, the definition of a sandwich certainly does. By definition of the dictionary, a sandwich considers a split bun with filling as a form of sandwich. It's a rectangle/square situation, but it still allows hot dogs to be classified as sandwiches.
[P1] A hot dog is not defined the same as a sandwich [P2] A hot dog should not be defined as a sandwich
Rejecting the premises
The standard home chip or noodle sandwich involves folding a single slice of bread in half.