You talking about the metal drum? Seems like that's necessary. He explains why in the video, tldw: it radiates heat which cools the exhaust, causing it to sink, and this starts pulling air through the combustion chamber. He calls it an air siphon at one point. Yeah you lose some heat from this, but without that siphon it won't create the jet furnace in the firebox. Maybe there's a way to engineer that without metal, I have no idea.

The goal is to have the fire drive a high airflow, both to give itself oxygen, and to pass the exhaust through a long path of heat absorbing dirt. The metal drum does this by passing the hot exhaust up through its center, then rapidly cooling it as it falls back down along the metal surface. The difference in density drives the airflow. The drum needs a high thermal conductivity to be able to maintain this temperature and density difference, and this is also the primary way the heat is transferred to the living area. The earthen part gathers up the remaining heat to increase efficiency and retain heat for when the stove is off, but most of the heating is done immediately through the metal.

Metal has better thermal conduction (transferring heat from one end to the other) the brick/clay/mud is there for thermal insulation to trap more heat and keep the metal conducting even after the fire has gone out