Dictionary entry for sandwich is " two pieces of bread with food such as cheese, salad, or meat between them " and I see two very thick crust slices with food such as cheese salad or meat between them.
I am going to say yes and make this my hill to die on!
if you define sandwich as "food, where there is some filling between two thin slices of bread", than it is not a sandwich. This is more of a burger, than sandwich.
I don't think this qualifies as a burger. My understanding is burgers are ground meat patties on a bun, this appears to me to be a standard sandwich made with two very thick crust slices.