The comparison of fog with a cat sets up the imagery that is created in the reader's mind. Anyone who has ever seen a cat quietly walking along its way will understand how silent the arrival of the fog is.
Fog, by its nature, comes when the air is very still with no wind or disturbance, just as a cat may come in "on little cat feet." Because the fog remains only as long as the air remains still, it is very much like the cat that "sits looking...on silent haunches." When a cat has finished surveying one area, it quietly rises and "then moves on" to its next resting place.
Diction emphasizes the movement patterns of the fog and of the cat. The repeated "t" of the "little cat feet" points out the definite steps being taken by the cat - not showy or overdone, but present. In contrast, the smooth connections of "n" and "m" sounds reflect the gliding departure of the fog when it "then moves on."