ROB: Kibuyi is the same issur whether extinguished completely or if the fire is only reduced. In both cases it is forbidden when not for ochel nefesh and permitted when O”N is involved. That is why the Rema permits completely extinguishing the house fire. I quoted an Igros Moshe to this point above, but Mishna Berura and earlier sources are also clear. The only difference in our case is that with an oven there may be justification to reduce the flame to simmer as ochel nefesh, but completely turning off the fire would NEVER be ochel nefesh because if the food needs no further cooking it could be completely removed from the stove.
The Aruch HaShulchan was niftar in 1908, and there was no electricity in small towns in Eastern Europe at the time.