Here's a copy I found online of exactly the same table I have in my strength of materials textbook... The equations you've posted don't look right:
One of the easier to explain uses for the modulus is designing/optimizing tops and braces (depending on how much of a background in engineering/physics you have or want to learn.) Modulus can be thought of as a measure of stiffness (the degree to which a material will resist flexure when stressed.) Among other things, you have a true empirical strength to weight ratio for each piece now. These data can be used to tune the thickness of the top to get a obtain a consistent response while safely doing so. As you can see from the beam bending formulae, all else being equal the resistance to flexure is a cubic function of thickness... Without first knowing the modulus if you were to make every top the same thickness, some could fail while others would have terrible response and tone.
I'm not personally a big fan of calculating every last element in a design even though I have the tools and education to do so. At the very most I personally suggest calculating the top thickness plus 15% to 20% as a design safety factor as well as a few of a the most critical braces. For example, the two members of an X-bracing system, or the cross member of a classical guitar that uses a fan bracing pattern. it gives you improved consistency and a good starting point for any build.
One last thing: The "long grain" measurements are much more useful than "cross grain", simply because that's where most of the load bearing takes place. If you're plugging everything into Finite Element Analysis software it will make a slight difference.