The intermolecular distance between the molecules are much greater than the diameter of the gas molecules so we neglect their volume compared to the volume of container. "The rapidly moving particles constantly collide among themselves and with the walls of the container. All these collisions are perfectly elastic. This means, the molecules are considered to be perfectly spherical in shape, and elastic in nature". How then are molecules thought to be perfectly spherical in shape although its volume is neglected.
The basic explanation that you've recited for the Kinetic Theory of gases is trying to present a simple complete and consistent model which explains the observed behavior. Thus to give a consistent perspective it is easiest to think of gas molecules as elastic spheres. Of course, the assumption about the negligible size of the molecules does indicate that the shape of the molecules is irrelevant to the volume of the gas. But if you consider the molecules as having edges, or different moments of inertia about the three axis then the "simple" model gets too complicated for "simple" mathematics. Think of the all the additional variables that would be needed.
The basic model neglects other factors of course. In the real world gravity plays a part. The atmosphere decreases in density as the altitude increases. So the basic model is trying to illustrate the key factors necessary to understand the kinetic theory of gases, not all the factors.
Edit - The basic gas law PV=nRT has been modified by a number of expressions where correction factors have been used to make the equation more accurate and to give the equation more dynamic range. See some of the equations in the following wikipedia article.
I am not a master at this, but from what I know, the volume of the molecule necessarily need not depend on the shape of the molecule. Hence the volume of the molecule does remain negligible when compared to the volume of the gas. Plus, if you must have read about the Vanderwaal's Real Gas Equation although not flawless, accounts for the correction in the Volume of the molecules which we assumed to be negligible in case of Ideal Gases. And as such, in real life we won't encounter a perfectly ideal Gas. So the Real Gas Equation shall help you considerably with your doubt. Hope you understood:-)