It’s using bread as a vessel to deliver its ingredients for consumption, and both bread and ingredient are eaten together. That is the simplest definition of sandwich, and this also means a Beef Wellington is a sandwich too. Deal with it.
The fact that it is one piece of bread instead of two is irrelevant, as one subset of sandwiches, subs and hoagies, are also one piece of bread. It is a hoagie, just like this kind.
A hot dog simply has exactly one ingredient.
And having one ingredient does not disqualify hot dogs from sandwichhood, as many well-documented sandwiches have only one ingredient too. You can have an onion sandwich, a grilled cheese, and so on. Furthermore, you can make a sandwich with zero additional ingredients, with the fabled toast sandwich.
Any way you slice your bread, a sandwich is a sandwich, and a hot dog is sandwiched between the borders of the definition.