You've never participated in an MMO "zerg" before, have you? Or better yet, pay attention to zombie movies and TV shows. It seems like you're scoffing at the threat of overwhelming by numbers simply because the numbers aren't well-armed. My thoughts? Facing superior numbers sucks regardless of how well-armed they are, especially when those numbers are ruthless and conscienceless. You can only take out so many of them before you are so overwhelmed you can't even defend yourself with whatever superior weaponry you have in your possession. We got a hint of that during the episode - those men were screwed until Dany and her dragons showed up, and even then it cost them several men, Viserion (yeah, that was about the Night King's arm and accuracy more than it was about the numbers), and they barely escaped until Jon sacrificed himself for their safety.
Going back to the MMO example, the whole point to playing a "minion master" Necromancer is the minions are disposable - you throw them at your enemy indiscresionately, and if they get killed, you make more. That's the terrifying thing about the Night King's army - he has superior numbers he's willing to throw away, and has the possibility to make more.