It definitely needs to be defined. Using only the paper, I assumed from the previous definitions that (a b . c) should be parsed as (x y) where x = a and y = b . c which can be re-written using only pair notation as (x . (y . nil) ) or (a . ((b . c) . nil)) and this made it very confusing to try to figure out what is meant by "improper."

Even if a definition for the notation (a b . c) is added, an example of such an improper list fully broken down into pairs would certainly still be appreciated by us readers who don't already think in Lisp :)