According to Merriam-Webster, a hot dog fulfills all the necessary requirements to be a sandwich, therefore it should be considered a sandwich. Rules are rules. Here's what the snarky dictionary (and arbiter of all things) says:
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.
Others think the rules-based explanation is bullshit and doesn't hold up. Hot dogs are hot dogs and should be recognized as their own special thing. If we're using dictionary-based definitions to determine legitimacy, let's see how bread is defined:
bread - a usually baked and leavened food made of a mixture whose basic constituent is flour or meal
Based on this definition, the tortilla can be considered a kind of bread. Then, does that mean tacos are sandwiches? Burritos? Quesadillas? What about bao buns? Dumplings? Is this really the world we want to live in? It'd be sandwich anarchy.
People need to see the light and realize hot dogs are just hot dogs. No need to make things complicated.