That looks like making "left" and "right" make the player turn left or right(Edit: clarification: left or right relative to the direction they are facing, not the client's view), I interpret the original question of making the player's icon face in the direction they are moving.
In that case, ensure that their icon is a movie with every desired direction having an image(a movie can be one frame long, and is the only way to support directions in an icon file)
After that, the player's dir var will set what icon direction is shown. Also, the default function of /atom/moveable(/mob)/proc/Move() sets dir automatically.
So, simply give them a movie for an icon, if you don't want them animated use 1 frame, and then set the directions you want and create images/animations for them.