This picture repeated from above:
KL0688 shared some more information on the situation. The hiker who fell went up the Mt Whitney Main Trail, and camped with his two companions near Consultation Lake. Saturday morning, they continued up almost to Trail Crest, and parted at that point, with the two heading back down the main trail.
He continued on up to the summit. Then he proceeded down via the Mountaineers Route, taking the "Easy Walk-off" traverse from the summit slope eastward toward "The Notch". There is a satellite image showing the two routes on the Whitney summit here.
The accident occurred just left of the point where the "Final 400" red line meets the purple "Easy Walk-off" line.
He slipped or tripped, losing both ice axes in the process, where the traverse path needs to descend 5 or 10 feet to clear a bare granite "nose". In the picture above, it is horizontally just below center, and a little left of center. In the current conditions, the granite below that point is completely covered with ice/snow. Without any ice axe, there is no way he could stop the slide. Other hikers using the "Final 400" route reported it was extremely icy, so it took them a long time to descend, even using ropes.