Yes, by the term "normalizing constant" in this context is clearly meant a constant such that when it is multiplied by the vector in question, that vector would then have a norm length of one, which of course means that you should have
a=1/norm([Inv_M_Theta(1,1) Inv_M_Theta(2,1) Inv_M_Theta(3,1)]);
Another worry for you is which norm are they referring to here, the L2 norm which you have used here or another norm: L1, L_infinity, etc?
Also you need to make sure there is a proper understanding of the order of elements in I(4), I(5), and I(6). You have assumed they are Ixy, Ixz, and Iyz, respectively, but they might be some other order such as Iyz, Izx, and Ixy as in vector products.
Finally, you need to consider the accuracy of values in I. You give them to only three or four significant digits, but perhaps they need to be given more accurately than that to achieve the results you seek.
Note that you can simplify your notation by writing:
M_theta = [I(1),-I(4),-I(5);-I(4),I(2),-I(6);-I(5),-I(6),I(3)];
a = 1/norm(Inv_M_Theta(:,1));
instead of what you have.