If the shoulder is the axis, it's a crappy punch, and in that case, I would say hand size matters. For a well-thrown punch, the body is very much a factor, and has business here.
It makes sense, it's just a simplification, since you would guess that integrating a human body is problematic. The rest of the body is not stationary, which is why I think you're confused. When throwing a hook, the entire body is rotating.
I estimate the rod to be about a meter, maybe a bit longer (distance from spine to hand), but I think he did it a bit too long TBH. He also forgot to divide a term by 2 (the moment of inertia for the hand), but that's not all that important.
Now if the guy is punching while moving backward, throwing a straight with no body behind it, then hand size might matter, but these are rarely KO punches as it is and we're talking about guys who know how to put their mass behind strikes, not just their arms.