I am aware that there are some common use definitions that will define barefoot as simply a "naked" foot. Those definitions are from a different era. The definition is slightly different in modern times as it reflects the changes in foot coverings that now exist. There are "naked socks", 1/2 socks, liners, etc. that technically are foot coverings.
The intent of the reference and its broad regulatory interpretation is to provide a basis upon which an agent of the air carrier can intervene. It also requires common sense in its application. No airline is going to bother a passenger for being in their socks or nylons at their seat, or even foot naked while in their pod. However, when a person sticks their foot up as this person has done, the airline can justifiably intervene.