Walking “properly” is a topic of interest for me. I believe it can be reduced to one main constraint: ensure most effort is spent by abdominal muscle in your core, with limbs and the (importantly) neck as relaxed as possible. Other characteristics of “proper” walk naturally emerge as the easiest way of following that constraint[0].
I find that walking “properly” wakes me up, has some positive effects on my well-being, and can be difficult at times. Unevenly paved surfaces (like some cobblestone pavements) seem to complicate walking “lazily”, forcing me into the proper way of walking.
[0] IMO articles like TFA tend to focus on those “cosmetic” characteristics, thus entirely missing the point.