I think "clean" is intended relative to other wood-burning stoves. Because this design of stove burns at relatively high temperature, it yields more complete combustion and emits lower levels of particulate.
This doesn't sound right to me, because there's heavy soot production whether hot or cold stove. Are you sure it's not just because a large masonry stove (and its long chimney) has a lot more surface for soot and particulate to stick on compared to e.g. a tiny portable one?
But when we talk about burning wood cleanly we're really talking about smoke -- and that's almost entirely organics (including large amounts of carbon monoxide, methane, and VOCs) which will combust given sufficient heat and oxygen.