I'm guessing it is the hatchback? If so, how does it qualify as a hatchback?

It's the rear hatch.

Hatchbacks are cars that have a flip-up hatch or flip-up tailgate. They're kind of like wagons, but with a smaller load area.

I guess that's what makes a Yaris 3 or 5 door a hatchback.

doors 12 - font doors
door 3 - boot lid

doors 12 - front doors
doors 34 - rear doors
door 5 - boot lid