I think what they're trying to say is that there are regimes in which the HSD actually shunts energy from one electric motor to the other (i.e. one of them is "braking" and acting like a generator and the other one driving) and a big part (maybe the majority even) of all power goes through that path. This works even if the battery is empty, because the electricity isn't coming from the outside, it's coming from the spinning ICE.
Exactly. The vast majority of the launching torque comes from the electric motor, even if there is no battery at all.