The closed end does seem to be the top, because of the orientation of the pockets on both sides. The thing that goes inside must have a circular end, but is also clearly wider than that end (because the bag flares out), while the other end is small enough that the leather strap will fit around it to secure it inside.
But at the same time, it has what seems to be loops for hanging it horizontally off an equipment belt, which probably means it can’t be that much longer than the bag (cover) itself. And a strap to carry it open-end-down over a shoulder.
I can’t think of anything that would need/fit all of this, though
