The author could've made it somewhat easier, though. Keeping the unused variable (so still keeping the drop) it can be reduced by 1 operation, but the logic of what's on the stack and managing it is simplified:

  drop dup dup * swap abs - swap dup * +

  operation : stack
  (init)    : x y z
  drop      : x y
  dup       : x y y
  dup       : x y y y
  *         : x y (y^2)
  swap      : x (y^2) y
  abs       : x (y^2) |y|
  -         : x (y^2 - |y|)
  swap      : (y^2 - |y|) x
  dup       : " x x
  *         : " (x^2)
  +         : y^2-|y|+x^2

The author's version requires rot_3 in order to deal with performing the computation in an awkward order. This version deals with each variable in order and in a more natural way. And replacing `dup * ` with `square` simplifies it a bit more (which is what you'd do in a language like Forth, you factor common operations into new words):

  : square dup *;

  drop dup square swap abs - swap square +

  operation : stack
  (init)    : x y z
  drop      : x y
  dup       : x y y
  square    : x y (y^2)
  swap      : x (y^2) y
  abs       : x (y^2) |y|
  -         : x (y^2 - |y|)
  swap      : (y^2 - |y|) x
  square    : " (x^2)
  +         : y^2-|y|+x^2

Down to 9 ops, and reasonably clear at this point.