There's not only one story on the internet about people whose hearts started racing during the Butcher fight in D1. So yeah, story or, more precisely, context matters.
The Butcher also stunlocks you in melee, unlike most of the other enemies you have faced. He's not actually tough if you are prepared for him, but since most of the other challenges to that point were trivial, he comes as a big and thematic surprise. For a lot of us who were kids at the time, that dude was the scariest thing we had ever seen in our whole lives.
One: You see the mangled guy bleeding to death at the entrance of the Cathedral.
Two: He says to you that the village organized a raiding party to rescue the young prince, son of King Leoric, and that Archbishop Lazarus gone insane.
Three: The guy dialog is full of reference to the horrors they faced inside and how the whole group was slaughtered by a demon, called The Butcher.
Four: There is no extensive dialog here, just enough for you to be fearing this Butcher, of course the game doesnt tell where this Butcher actually is so you go from the first level to the level where the Butcher actually is waiting for him, the game milks the suspense as much as it can.
Five: You find a strange room, lonely, separated from other rooms (to focus the attention of the player as the room is isolated from the rest and increase the suspense), they did this on purpose as a rule for all unique quest rooms on the random room generator script they have for Diablo 1.
Six: Once the player go to investigate, he notices a small trail of blood coming from outside and the player can see the room seems to be actually filled with corpses and blood.
Seven: Imediatly the player remembers the guy dying on the begining and knows this is The Butcher room.
Eight: The player, confident, as he pretty much killed everything on his path to this point with little difficulty with a mixture of fear and confidence opens the door understimating The Butcher and that half his potion belt is empty and he didnt bothered into getting a decent weapon.
Nine: The Butcher says "Ahhh, Fresh Meat." when the player opens the door and The Butcher proceeds to pound the player relentlessly with stun lock attack after stunlock attack with a massive cleaver and seems to take a ton of punishment too, the player runs out of potions and die.
Ten: However, this is still on the begining of the game and the designers achieved the effect they wanted, they cant make a monster that is impossible to defeat at player level 3 or so because this will force the player to ignore it and have to backtrack afterwards and that isnt that fun. They make The Butcher, strong enough to kill dumb players but weak enough to be killed by prepared players.
Eleven: Player turns back and kill The Butcher and as reward, gets his axe that is an unique weapon and pretty decent for early game, so every time the player opens the inventory, he will remember this fight.
Twelve: As result, this fight marks an impression on the player, he now knows there is dangerous shit for reals to take seriously on the dungeon and this encounter increases the suspense level at least for the next few levels. I would argue that they sort of dropped ball midway through the game because Diablo 1 starts strong, then the middle really fails to ramp things up and keep momentum but it ends on a strong note again.
Yeah, sure enviroment design, storytelling is completely useless for hack and slash games... hummm...hummm... maybe if the rest of the Diablo clones actually learned a thing or two from the design of Diablo 1 they maybe would end better for it.