Hi Dushin,
maybe I can tell something about this.
There are some different kinds of cooking places in this time period. In western central europe the two most different ways are the fireplace with chimney and the “black kitchen” without chimney. As you mentioned, in the black kitchen the smoke will go through the roof of the house. Those houses has only one story/level and under the big roof there is much place to store grain, hay, straw and such stuff. Like an somewhat open multi-level attic. If the smoke from the cooking place goes upwards, it goes through all of those stored stuff and expells vermin/bugs/rats etc. This was very common mostly in rural areas till the 16th century and onwards. Those fireplaces have only a kind of spark-shield above them, instead of a real ceiling. On some days, all of the house was filled with a bit of smoke and it burns in the eyes, but this method must be very efficient, because it was used for several centurys. I don’t have to write much about closed fireplaces with chimneys. I think in the game they mixed up some things… one additional big error about that: They don’t cook OVER the fire, but IN the fire, exept of caldrons and skewer. In both kinds of fireplaces, there would be a sort of stone platform, sometimes with room for wood and stuff under it, and ON this platform they make a fire (not IN or UNDER it like in the game). If there was enough embers, they put the cooking pots in it. To regulate the heat, you can put it more to the fire or put it away. For this reason, many of the cooking pots have small legs. I think in the game they mistaken this, too.
As some of the others say, the round oven in the living area was fired from the kitchen on the other side of the wall throug a firehole. In houses with a “black kitchen” they usually have no chimneys, but the smoke goes through the firehole in the kitchen.
Greetings, Tobias