Definition: frankfurter; especially : a frankfurter heated and served in a long split roll

The word hot dog refers either to the sausage that you buy squeezed in a plastic package with 7 or so of its kind, or to the same sausage heated and served in a long split roll.

When it's served in the roll, it's also a sandwich.

We know: the idea that a hot dog is a sandwich is heresy to some of you. But given that the definition of sandwich is "two or more slices of bread or a split roll having a filling in between," there is no sensible way around it. If you want a meatball sandwich on a split roll to be a kind of sandwich, then you have to accept that a hot dog is also a kind of sandwich.

You could hinge your anti-hot-dog-as-sandwich argument on whether the hot dog sausage qualifies as a "filling," but if you choose to interpret filling narrowly as only "a food mixture used to fill pastry or sandwiches," rather than broadly as "something used to fill a cavity, container, or depression," then you're not going to allow any single-item filling to qualify a food item as a sandwich—which means there can be no thing as a peanut butter sandwich or a bologna (or even baloney) sandwich.

Hence, a hot dog is a sandwich.