We can see that is axially symmetric from the Eq of slide 29 since it is a diagonal matrix. Furthermore, it can also be seen since the symmetry parameter is zero (which means that we have axial symmetry).
An object is axially symmetric if its appearance is unchanged if rotated around an axis. In this case, we can see that is axially symmetric since the coordinates of the two electrons clouds are (0,0,z) and (0,0,-z). Thus any rotation on the x and y-axis is trivially equal since they don’t depend on this axis. On the other hand, a rotation will lead to an exchange between the two elements’ original position.