There are many styles of functional programming; the thing they have in common is that they all use first-class, high-level functions to implement features which other languages might implement via special-purpose syntax, bytecode, compiler passes, etc.

The "lambda the ultimate" papers are the classic example of using functions to implement a variety of language features, including jumps. Hence the author's claim that functional programming is an "inside-out" approach is more of a question of style than of paradigm.

For example, even simple function composition can approach the clarity of imperative code for following a step-by-step process. The result tends to look like UNIX pipes, although traditionally they're read "right to left" (but you can trivially define your own composition function which goes the other way).

Here's an example of the author's task, written in a compositional style rather than an "inside out" style:

    heatedOven = preheat 175 oven

    preparedPans = grease . flour $ pans

    flourMixture = whisk . add flour . add bakingSoda . add salt $ smallBowl

    creamedMixture = until (all [light, fluffy]) . cream . add butter . add whiteSugar . add brownSugar $ largeBowl

    bananaMixture = mix . add bananas . repeat eggCount (beat . add egg) $ creamedMixture

    batter = stir . add (chop walnuts) . repeat (size / spoonful) (add (spoonful flourMixture) . add (spoonful buttermilk)) $ bananaMixture

    baked = take . wait 30 . add (add batter preparedPans) $ heatedOven

    cake = take . wait 10 . add baked $ dampen teaTowel