Class based extra damage from Assassin/Harper/PDK/CoT/BG doesn't apply unless the hit does at least 1 physical damage before the damage adds.
So Hate Engine never takes it. I tested on a toon with 5 PDK levels (+magic damage) by hitting War with a dorky bow with 1d6 electric infinite arrows, he took the electric but zero physical and no magical. Then hit him with an actual weapon that did physical damage, he took the extra magical. Zombies outside the keep took the extra magical from the bow.