Hmmmm, that's something I wish I had covered. I think it helps to think of the monster moves as more like the GM moves than player moves: things that you use to set up danger for the players.
I never took monster "moves" to be literal Moves that you'd just lay out, like "BOOM you're suddenly dead from poison, better luck next time." They just tell you how the monster acts and what sort of things it does. Like, the deep elf attempts to poison someone. The basilisk attempts to turn you into stone, you gotta Defy Danger maybe, or figure out a way to avoid its gaze. Things like that aren't just said without a setup: you first describe the deep elf applying a sticky black goo to his blade, that sort of thing.
I always run monsters in Dungeon World like any other game. They show up, they act according to their description, and the players try to kill them. It's not like their moves give them special crazy powers; the moves just tell you what sort of creature you're dealing with: is it sneaky? brutish? conniving? That sort of thing.