Just making sure I'm playing this right, as soon as a dwarf unit leaves play I deal the damage for Dwarf Rangers.
Ex: My opponent starts an action LIFO stack by playing a unit from his hand on his capital phase. I respond by using the Grudge Thrower action, which makes me sacrafice a unit and pay 1 resource to activate the action. Now, since I do both in order to trigger the action, a unit leaves play while adding actions to the LIFO stack. So, this activates my dwarf rangers instantly at which I assign a damage to my opponent's unit or capital. I do this, then it is his turn to add actions the the stack. Everything else resolves as normal but since the dwarf rangers is a forced effect it goes off during the triggering stage of the LIFO stack.
Let me know if this is correct.