Partly based on the style (age) of the building I think it could well be structural, but to find out I think you'd have to take a look inside the ceiling beneath the stairs next to it to see how well the half landing is fixed to the wall. It certainly wouldn't have had a turned post like that originally - there would more than likely have been a stud wall instead which may well have (partially) supported the half landing. The problem with this sort of structure is that even if the stud walls don't start out as structural they can end up carrying part of the load as the building settles, etc over many years
Of course you could always stick an Acrow prop under there, cut out the post, and then take the pressure off the prop (screw to the underside of the stair first, not the floor, leaving 10mm of slack on the thead). If it doesn't move over the course of a few weeks then you probably don't need that turned prop. If it does move, you push it back up and replace the prop
