"shut down" == "making them give up".
I'm not a shrink so I'm not going to psychoanalyze, or pretend I have that ability to win an argument. You either have standing in a disagreement or you don't. Shutting down the discussion isn't "winning" the argument.
btw, a true narcissist is hard to diagnose. They are exceedingly good at hiding it if needed an have no guilt about it. So yeah, labeling people for sake of "winning" isn't "winning".