Space filling model for nitrogen molecule
Yes, two spheres with a radius of 155 pm and the distance between the center is 110 pm.

The axis in that picture is not aligned, that's why you get an error. Here's a picture with aligned axis and van der vaals spheres produced in Avogadro:



The corresponding *.xyz:

2

N   -0.55   0.0 0.0
N   0.55    0.0 0.0


I'm also unable to follow your math here. height of the molecule should be $2\times 155=310$ and length should be $155\times 2+110=420$ so height to length ratio should be $0.73$, you got $0.72$ which is pretty close.