You´re quite right, Franco!
Typical Scandinavian & German design common between 1860-1910.
The extension on top of the cumbustion chamber is actually a heat extractor one could purchase as an add-on to a simple direct draft stove... The top of the barrel (over the heating compartment) is split in two lengthways, leaving a gap on the top so that the exhaust travels up in the front of the barrel - providing max. radiant heat the room - and down in the rear until it reaches the stovepipe.
The example in the foregound dates from the early 1900s and comes with a radiant lower half, while the upper part creates a convective flow between the cast iron core and the sheet metal coat. The one by the window in the background works on the same principle but is a 1870´s radiant-heat-only-model.
btw: rated 20-24K BTUs, would hold approx 10lbs of coal