I had a little trouble completing this quest because the key wouldn't drop off the Azerite Extractor Mk. II. Killed it 3 times, no key. Tabbed out to look it up and came back to a dead character, but noticed Drelix Goldspark is the one who killed me. So I killed the Azerite Extractor again a couple more times with no Drelix.
Finally, I used potions and cooldowns and killed it as slowly as possible until I saw that Drelix Goldspark was hitting me too. I killed the Extractor, then got to kill Drelix, and finally I had the key.
I don't know if killing him slowly worked, or if I just needed to wait until he spawned with the machine, but you have to actually kill a goblin named Drelix Goldspark, not just the machine.