In my opinion, this picture's 3-dimensionality is primarily the result of the marked change in contrast between the foreground/middleground and the mountainous background.
The decreased contrast in the background is due to the haze, which is probably due to impurities in the air that naturally arise over a forest in the heat of the day.
A second contributor to 3-dimensionality (depth) is the shape and direction of the pathway and the position of the woman on that pathway, which is all related to the geometry of the path in the foreground/middleground.
The haze and the resulting loss of contrast in the background is quite noticeable when compared with the high contrast coloring of the man, so you unconsciously recognize that the background is far away, because you recognize the significant loss of contrast.
In the B & W version you don't recognize the background as being hazy. It is hazy, but you just don't recognize it as hazy - so the feeling of depth just isn't as pronounced.