he doesn´t need a clutch to put the gears in and the stick moves in two directions only. back and forth. when the driver wants to shift up he pushes the lever towards the dash. the engine then will cut ignition for an instant while a hydraulic unit changes the gear for the driver. after the gear is in, ignition comes up again. that all takes only a split second.
btw, shifting down is pulling the stick to the back. the reason why you might see the left leg working is that he brakes with it. i did not watch it that closely yesterday so this is just an idea, but maybe?
on the other hand, the car may also be a standard manual shift. the M3GTR for the ALMS is manual shifted and is basically identical to the scheid BMW. i´ll browse the net to find it...