Sorry, but that is simply wrong.
And yes, the inverse square law is strictly speaking only true for point sources. But it is an extremely good approximation once you are much further away than the size of the source (a distance ten times the diameter of the source is usually totally sufficient).
I had to re-derive it for a perfect cone to be sure. You are correct; at a distance where the size of the cross section of the beam is significantly larger than the source, deviation from inverse square becomes negligible.
EIRP is describing that the total flux through a sphere at a given radius is constant regardless of the beam shape, but we are only interested in a specific cross section and are not accounting for the rest of it.