The idea that we should classify food by shape is clearly erroneous. Our food classifications should be based on method of eating, not by shape! A sandwich is any food that uses a carbohydrate to protect your hands from a messier food, so that you can eat it at a card table without getting your hands dirty (a la the origin myth). Let's go through the things here:

Pizza: Yes

Sushi: Mostly no (the carbs don't protect you from the insides, the seaweed does)

Pumpkin pie: No (unless eaten with hands, without falling apart)

Quesadilla: Yes

Toast sandwich: No (inside is not messier)

Victoria sponge: No (eaten with fork)

Hot dog: Yes

Sub sandwich: Yes

Slice of pie: No (unless eaten with hands)

Falafel wrap: Yes

Pigs in a blanket: Yes

Enchilada: No (the one pictured has cheese and sauce on the outside)

Quiche: No (unless eaten with hands)

Cheesecake: No (unless eaten with hands)

Soup bowl: No (I'd love to see you try)

Falafel pita: Yes

Deep dish pizza: If eaten with hands

Salad in a bread bowl: No

Key lime pie: No (unless eaten with hands)

Calzone: Yes

Corn dog: No (if held with stick)

Pie (whole): No (good luck)

Dumplings: Yes (unless they have sauce on them)

Pop tarts: Yes

Uncrustables: Yes

This is the best and most accurate method that actually provides a strict definition that lines up with my intuitions—the cube rule is fun, but you're really gonna claim that a subway sandwich isn't a sandwich?