He is giving an instruction on how to throw punches, he starts in slow motion to show the extension of arm and shoulder, then he speeds up and starts to show combinations. Near the end you get a chance to see some very good work and a glimpse at how his style overwhelmed.
No, I'm pretty sure he's doing "isometric" exercises. This was something of an exercise fad at the time and consists of doing "resistance" training without any kind of equipment, simply by going through various motions with the muscles tensed as tightly as possible.
Isnt there a couple of clips of Dempsey doing the same thing in training for Williard and The Orchard Man
I also seem to remember once seeing a clip of one of the Gibbons brothers (I forget which one) shadow boxing pretty much the same way. Actually, I don't recall ever seeing anyone from 100 or so years ago shadow boxing in a "modern" way. I guess, they just did things differently back then.
Perhaps a warm up? In Dempseys case I think I remember him doing it outside part of this clip that spawned his famous back bicep pose. Then theres one that's a quite extensive indoor calisthenics training routine where he does it again. It looks alot like there emulating the weighted wall pulley work which was popular then but I also believe Jack covers it in his explosive fighting/punching technique book. Looks like a follow through move part of a warm up to punch properly with the shoulder rotation in the beginning
Now that you mention it, it does indeed look a bit like the same movements they used in the wall pulley - so maybe they were simply attempting to do something similar when shadow boxing? No way of knowing, of course… but it sounds like a plausible explanation.
I have always wondered, how Greb could play handball - without, seemingly, missing the ball even once - at a time when he was completely blind in one eye! With no depth perception, how is this possible?