Old Man Henderson is a problem not of game system but of game philosophy; Dungeon World tries to pre-empt that philosophy.
Some people will say "it was actually Trail of Cthulhu" but I think that's part of the status of Old Man Henderson as gaming urban legend that gets added onto. It was Call of Cthulhu, because you don't get to test to avoid SAN loss in Trail of Cthulhu, and you can't survive 15 SAN loss - Gumshoe likes to work in small numbers, SAN is intended to portray long-term degradation (short-term shock works on the STAB or Stability track), you're a goner at 0 and nobody can start with more than 10 or possibly 12. Call of Cthulhu's SAN works on the 0-to-100 scale.
I mean, maybe it's a game of Trail of Cthulhu that the Keeper was playing like Call of Cthulhu? That happens; people will try to play Dungeon World like D&D, too - just because the rules forward a particular philosophy, people can still break them to play as they please.
There are three pillars of philosophy that hold up the idea of Old Man Henderson: the GM's plot as precious thing, the GM as neutral arbiter of an adversarial situation, and the secret player power.
The GM's Precious Plot - "DO NOT pre-plan a storyline, and I'm not fu[nn]ing around"
Most Apocalypse World derivatives will take the swears out of that, as I've had to, but the idea remains constant. It doesn't mean "don't prep" - you absolutely should prep, but what you should prep are groups and places and philosophies. You shouldn't prep "a line" - the bright thread of prophecy that when severed plunges the world into darkness, or a single narrow path of actions you have no idea how to act outside.
Here's a scenario in Dungeon World where some PCs do the Henderson thing, destroying what would might be viewed as the first vital step in a story of (perhaps) a king who craves the power of antiquity but will call up things he cannot put down. But their violence was only against the king's agents; the king still craves. Old Man Henderson, an agent of unreasoning violence and destruction, can only shut down a front by annihilating it utterly -- and if it actually comes to that point, the GM has got all the mileage they need out of that front anyway.
Judging a Rigged Game - "Play the game with the players, not against them."
The philosophy can be summed up, perhaps unfairly, as "prepare adversarially, run neutrally". Prepare a threatening place full of threatening things, but when it comes time to game, put the idea of threat aside and run fairly according to the rules and your own precedent. In the worst case, this can often lead to an odd sense of pride as a GM; pride that you built opposition that could take the PCs in a "fair fight". Old Man Henderson comes into this and either plays by rules that disproportionately advantage the PCs, or takes improvised actions that the GM has to adjudicate in the moment and are fair game for PCs to argue over their relative fairness.
Apocalypse World and its derivatives tend to point away from the dispassionate style of playing. Name everyone, give everyone life, but also be a fan of the players' characters - neither of them are dispassionate things to do. Nothing limits what the MC can do when the game's on - "make as hard and direct a move as you like" is a common refrain - but the MC also doesn't get to be protected by a principle of impartiality, and is accountable for their taste to their players. Everything the MC does to you is because they want to.
Old Man Henderson can take refuge in audacity, because the GM is trying to be the disaffected reasonable judge and is thus obligated to take him seriously. A Dungeon World GM is a participant in the conversation and doesn't have to play down their own desires.
The Player-Agnostic GM - "Offer an opportunity that suits a class's abilities"
Another element of the Old Man Henderson mythos is his 300-page backstory, written partly in Enochian, lost tongue of the angels (or something like that). Apparently it justified everything he had access to, even though the things you have access to are kind of controlled by the character creation process, and you can't ignore build points with a 300-page backstory, any more than you can ignore hit points because on page 250 it says you submerged fully in the river Styx and are invulnerable.
But the idea here is something I've seen elsewhere - that the GM should leave the players to manage their own character sheets and shouldn't concern themselves with what's on there. I can kind of see the wisdom of this, especially for novice GMs in a system with complex and volatile player powers, like a cleric's daily spell loadout in 5E D&D.
However, it really falls apart in the face of the demands of Apocalypse World and its derivatives. If you don't know what moves a player has access to, through the combination of basic moves and their playbook, how can you possibly judge whether they've made a move or not? How can you be a fan of them and offer them opportunities without knowing what they're capable of? How can you activate their stuff's downside if you don't know what their stuff is or what its downside is? (Seriously, if you're running Dungeon World, even as a one-shot, have a second copy of the playbooks that you can keep for yourself as GM reference. You'll thank me, unless maybe your play surface is baby-sized.)
Nevertheless, Henderson can persist.
Old Man Henderson was born out of a desire to ruin whatever the GM was planning. That desire can still exist in players, out of spite over past transgressions or just because it's how they choose to approach the game. It doesn't matter the system that it's in.
But in an Apocalypse World system there's less to hide behind, if nothing else because the GM is supposed to be a fan of the players, needs to know what they want out of the game, and has the power during play to give it to them. Eventually it's going to come out what the Old Man Henderson player wants to do, and everybody can confront it there.