This whole fucking discussion is why I hate philosophy.
WHY define a sandwich. WHAT DO YOU GET out of defining a sandwich. WHAT IS THE PURPOSE of defining a sandwich. Yet here we are, "a sandwich to me because" "but not this because flatbreads" "socratic method through sandwiches" EAT A FUCKING DICK.
Definition is a linguistic exercise. Linguistics is the art of communication. The purpose of defining a sandwich is not so that you can contemplate the fundamental nature of "sandwich" it's to communicate "sandwich" to someone else.
So is a gyro a sandwich? No, a gyro is not a fucking sandwich, a gyro is a gyro and if someone wanted a sandwich and you gave them a gyro, they would be confused. Is a gyro sandwich-like? Certainly, because when you visit 24-hour diners in rural America as "gyro sandwiches" because the way you communicate the concept of frozen gyro meat with iceberg tomatoes and yogurt to a trucker in Bismarck is by giving him an anchor ("sandwich") and a qualifier ("gyro"). This could also be a "philly cheesesteak sandwich" or an "egg salad sandwich" or a "monte cristo sandwich."
Is an open-face sandwich a sandwich? yes, an open-face sandwich is a fucking sandwich because it has all the known ingredients of a sandwich, but it is served in a way outside the norm. "open faced" (qualifier) "sandwich" (anchor). Note that more than one anchor is needed: "open faced" "hot" "turkey" "sandwich."
Is a hoagie a sandwich? yes, a hoagie is a sandwich because at one point it was a "hoagie sandwich" but the term became so popular that the anchor was dropped and the qualifier became the anchor. A "po boy" is also a sandwich as is a "philly cheesesteak" and, like the gyro, depending on where you are a "monte cristo" is a sandwich without needing to be a "monte christo sandwich."
So is a hamburger a sandwich? Fucking hell a hamburger is a sandwich, but you don't think of it as a sandwich because the qualifier in "hamburger" "sandwich" became such an anchor that it has prompted an entire industry of food on its own. But it's still a fucking sandwich. How 'bout a hot dog? It's got a roll split in half with something in the middle, right? BUT IT IS NOT A FUCKING SANDWICH because no one has ever called it a fucking sandwich, will never call it a fucking sandwich, and if you want a hot dog sandwich, be poor, be out of bologna, and have a sharp knife. Yet apparently this is a fucking thing that actual people actually talk about.
It quickly becomes obvious that the definition of "sandwich" is heavily dependent on context, which isn't surprising, because it's food, and food is one of the deepest somatic triggers of tribalism we possess. But "sandwich" is also so ubiquitous that it's a noun, a verb and an adjective. I can eat a sandwich. I can eat sandwich cookies. Wooden studs can be sandwiched between two layers of drywall to form a wall. It's a versatile word, so much so that it forms the shorthand of "thing between two other things" to anyone who learns English.
But a definition beyond that is subjective, context-sensitive, and UTTERLY AND COMPLETELY FUCKING WORTHLESS. Is a gyro a sandwich? Depends - does the guy you're telling about the gyro know what a gyro is? Does he know the word "sandwich?" Because if he knows neither word, you're going to have to take another tack.
And that tack will involve describing flat things with stuff in between.