Confusion calculating length of Kaiser window
This is just an empirical formula found by Kaiser for determining the necessary filter length for a given transition width. That formula is given as Equation $(7.30)$ on page $332$:
$$M=\frac{A_s-7.95}{2.285\,\Delta\omega}+1\tag{1}$$
I think that Kaiser came up with a formula for determining the filter order (hence without the $+1$ in the equation), and the authors of your book preferred to have a formula for the filter length, so they took the original formula and added $1$ to it.
Judging from some of your previous questions, you seem to be confused when it comes to the terms filter order and filter length. For FIR filters, filter length is the number of coefficients (taps). Filter order is the (minimum) number of delay elements necessary to implement the filter. It's just like with polynomials: their order is one less than their number of coefficients. E.g., a second-order polynomial has $3$ coefficients:
$$P_2(x)=a_2x^2+a_1x+a_0\tag{2}$$
Coming back to FIR filters, you always have
$$\textrm{filter length}=\textrm{filter order}+1\tag{3}$$