Are you hoping to do the Main Trail or the Mountaineer's Route (MR)?
During the first part of the video you mentioned, Richard and his group summit Thor Peak, which sits between those two trails.
Just after they summit Thor Peak, and from 6:54 to 7:28 on the video, the section of the Main Trail from Mirror Lake to the summit of Whitney (including Consultation Lake and Trail Crest) is either filmed and/or described (since the latter portion of that trail from Trail Crest to the summit is not visible from the top of Thor).
At approx. 4:00 on the video, only the latter part of the Rockwell shortcut on the MR appears to be filmed. What wasn't shown was where the shortcut begins, the brief Class 3 scramble to get up to it, and then the very narrow, though somewhat brief ledge that is the most exposed part of the shortcut.
So taking this shortcut will depend on if you're OK with a bit of Class 3 and exposure. Both of those had ended by time they began filming the last part of the shortcut.
A picture is worth a thousand words. Take a look at photos 6 through 13 from this
recent album of Bob Rockwell's, which show this same shortcut, including the narrow ledge and the Class 3 scramble. In fact, photo 7 shows our own Steve C negotiating the Class 3 section.

CaT