The standard walking example in the manual under "c_move" uses gravity.

http://manual.3dgamestudio.net/ac_move.htm

I see you used a similar code, but the comment mentions that the player models center must be really inside the model, and not below its feet or something, and the player must not be smaller than his bounding box, maybe that was your problem? The blue bounding box in your screenie looks wrong (too big).