I think the way they are describing this, they refer to "rotation" as simply the movement which occurs - how many degrees the segment rotates. As far as the long axis, that could be about the pelvis, the shoulder girdle, or a combination of the two, since they move differently during running. "Torsion" would be the twisting due to applied force... Not sure that would be the best word to describe things in this context.
I'm not sure how accurate that description is if you are using it for scientific purposes. For example, force is applied during the latter part of stand - force where? There is axial rotation occuring in even in the float phase of the running cycle (when the body is completely off the ground). And the axial momentum of the upper body actually seems to help rotate the pelvis to prepare it for the next stride.
What are the references for that cited within the book? Not a whole lot about torso axial rotation has been done. Hinrichs looked at this in the 1980's and wrote some very good things. Schache had some things published about this with regard to axial rotation in the pelvis a few years back.
Let me know if you need more info.