It is Bruce speaking in the footage - reviewing the training later with Coburn - telling him what he's doing right or not.
Further, that footage has always appeared to me as if they are working more on camera angles and how to look highly skilled at delivering strikes in movies - which is always intentionally exaggerated - than on a "jeet kune do for the street" session.
My conclusion is based on:
1 - how concerned Bruce appears throughout with (movie) camera angles and their timing.
a - he even does sound effects of having been struck, etc., throughout.
2 - also, there is the recorded assertion by Coburn, elsewhere, of a conversation along that line, which took place between him and Bruce, back when he and Bruce first met and Bruce mentioned to him the very issue Bruce is observed working with Coburn on, in this footage - on helping him rid himself of what Bruce had observed as that "flicky, flicky stuff" in Coburn's movie martial arts scenes in his "In Like Flint" movies.
Here is the dialogue of the above video, along with a more extensive version of said video, following...
Bruce: ...now watch this illustration, you GOTTA EXAGGERATE (the) bringing (of) the leg back (or of bringing) anything back, okay? Watch it again...you see - EXAGGERATE the pulling of the leg back: MAKING IT LOOK much more faster and more forceful...
[FormlessOne Note - they are focused on FORM (looking good) over FUNCTION (actual jkd)...
Further, my words in brackets there, and Bruce's words in caps, are my deliberate emphasis of Bruce's INTENT, but I believe I have a better than a solid grasp of speaking in Bruce Lee-eze, lol]
Anyway, on to the longer version of that "workout..."
Original YouTube Video Title:
Bruce Lee - kicking
Some Additional Notes of Mine:
1 Bruce's words regarding the above are near the end of the following video, starting at about 8:08 minutes, or so.
2 This video has close captioning (click on the three dots in a vertical line, all the way to the lower right of the video, and then on the CC in the box).
3 There is some irony here - in the "JKD training video" this video portion of said video is based on - on that Coburn movie fighting training footage - is mistakenly being presented as training in actual JKD.
But clearly, that footage depicts training in highly cinematic, or movie JKD.
Again, Bruce had merely been helping Coburn rid himself of that "flicky, flicky stuff" of his that Bruce had observed in Coburn's "In Like Flint" movies.
4 At the same time, Bruce was working on his own "relationship with" camera angles, etc.
5 Once more, Bruce merely isolating a thing towards working on it, specifically...
Further, he had been too secretive to allow his "real jeet kune do" to be caught on film - "why should I teach anyone...how to beat me..." he had noted, on more than one occassion.
6 Bruce merely being...Bruce.