Why is the wingspan length not added to the variables that the aerodynamics force R depend on?
The body is of a give shape and of a give angle of attack. The only variable left is then the scale of the body.
The author decided to use the chord length as reference length; if the shape is known and the chord length is known, all dimensions of the aircraft are follow from that. Alternatively he could have chosen the wingspan, tail height or any other length as reference length.
In page 38 of the book you're quoting, the derivation goes on replacing $c^2$ with $S$, the planform area of the wing, implicitly introducing the wingspan...