It may be that even if the main purpose of the brick part is not to have a supporting function on the floor joists for the floor above, it might have been built that way anyway.
But above all, it has probably served a fire protection function for the kitchen stove that was there in the first image.
However, be careful to check that it does not have a supporting function for the chimney and any ventilation duct on the upper floor! If the brick part continues on the upper floor, I wouldn't tear it down...