Local means with respect to its parent as opposed to global - with respect to world co-ordinates. If an object has no parent, these are the same. With nested objects that use position or rotation in a calculation, this can be important.
In this file the red sphere is a child of the blue cube, and the cube has a vibrate tag. Although the red sphere is moving in world space, in XPresso it seems to have no velocity because it is not moving with respect to its parent. The yellow sphere is also a child of the cube but has its own vibrate tag and in XPresso it has position velocity. Note that you usually have to enable animation refresh under calculate in the XPresso menu to see values change in real time (the vibrate tags have different seeds so they don't move in sync, which would confuse matters). In C4D, some things are absolute, some relative and some have the option to choose.
In the video, I think the guy is multiplying not adding - might affect things. Change it it the node drop down menu.
https://www.dropbox.com/s/4hatt1md69n8hbr/relative.c4d?dl=1
BTW position velocity is a vector - has X, Y and Z values. When you plug a vector into a real, C4D does the 3-way pythagoras conversion to a linear value automatically.