If you imagine the structure of the vortex in 3D based on the views from above and the side, you would probably end up with something like this. First, in a rotating system bunching and spreading in a horizontal direction cannot occur without viscosity, so convection in the perpendicular plane is limited to the Ekman layer at top and bottom where viscosity dominates, and also in the thin pillars where viscosity can also dominate. In this experiment the thickness of the Ekman layer is as thin as 1mm, so capturing the flow there in a picture is extremely difficult. The other parts of the fluid are hardly affected at all by viscosity, so rotate around and around the pillars as geostrophic flow. The only flow really visible from above was that geostrophic flow.