From the equation, the EFG tensor given in the video has axial symmetry in the PAS because V_xx and V_yy terms in the tensor are equal to each other (i.e. η = 0).

From the visual inspection of the toy model, the only part that matters is the electrons. Since the electrons lie on the z-axis and are equidistant from each other.

A simple toy model that is not axially symmetric is when the electrons are not equidistant from the nucleus and not aligned with the any axis.