[Update 18-04-2020]
This class has been renamed Warrior to better reflect it's unique nature in comparison to the classic D&D-ish Fighter.
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TL:DR

I am dissatisfied with the way most games portray the Fighter class/archetype. Often, not always, but quite often, the Fighter ends up being a "basic" character in more than one way. A vending machine for damage, dealt in the most blunt and direct way. The not-so-complicated tank option for beginner players. Boring, flat, largely useless outside of combat.
In the PbtA-verse this problem is less marked because the overall system encourages and supports a better exploration of the PC and the narrative surrounding them, but even the Dungeon World Fighter and the Apocalypse World Gunlugger end up sticking to the Dumb Damage Dealer stereotype as both focus their moves on combat and the direct use of violence.

I would like to fix that.

The Fighter

In Fantasy World the Fighter class is about violence but not necessarily violent per se. The Fighter is about the meaning of violence, the toll it takes on a person, the marks it leaves behind, the way it warps how the Protagonist appears to the world.

This Is My Weapon is a move that partly mimics the classic DW "Signature Weapon". Why throw away the baby with the water, right? Outlining the Fighter as the one with the badass weapon is a great idea! FW offers a bit more creative latitude out of the box, but that's it. The important difference is in the last section of the move, where the rules ask the Player to answer one out of three provocative questions...

Tell the World:

• a thing you did to get it, that you are ashamed of
• who gave it to you, and why it hurt you to accept it
• how you got it, and how it changed your personality

Out of the gate the Fighter is cast as someone that literally carries around a physical token of a past shame that still burns, or a past regret that still hurts, or a past turning point that shaped who they are now. All tied to the weapon. This is gold for the World, and goes a long way in helping everyone at the table (and especially the Fighter's Player) to think about this Protagonist as a multidimensional individual, a person that goes beyond being a proficient user of violence.

Not to Be Trifled With plays to the stereotype of the Fighter as powerful individual, but does so in an open ended way. The Protagonist could trigger it by smashing stuff, sure, but also by showing off their sick dance moves, revealing their beautiful body (or their scarred, impressive, deformed, whatever-makes-it-noteworthy body).

The Fighter is thus defined, at their core, as a person with a troubled past that on occasion knows how to take bold, confident, incisive action. Oh, and they have a cool weapon too!

From here on out, the Fighter develops as a person with a rich introspective life :P
Arcane Heirloom brings the weapon to life to offer guidance and counsel, but also reveals weaknesses and shortcomings of the Fighter's persona and makes them mechanically relevant as TAGs.
The Riddle of Steel asks the Player to express, always in regard to a specific situation, their opinion on what it means to be courageous or cowardly, with no neutral middle ground. Which one will you choose?
Veteran Scars invite the Player to bring the Fighter's past scars to life, both as a short tale of what happened, but most importantly as a meaningful memento of something important to them.

Bulwark adds to the "powerful individual" narrative, supporting a flashy play style. Ignoring Nasty effects means that when you decide to stand your ground, you STAND it. You don't go down, are not blocked, don't even look like the harm did much of a dent on you ... while under the surface you might be hurting quite badly. But you look fine and powerful.

Brute is the only move that straight out plays on the Fighter=Violence idea, but it does so by cranking it up to eleven. To trigger it you don't need to be violent, but savage. This could mean anything that the victim/witness might consider barbaric and uncivilised: pissing on their shoes, using particularly foul language, eating a live animal, etc. This impresses onto the witnesses the idea that the Fighter is a savage. Being a TAG this affects both the fiction and the active game-play, as there are many ways in which anyone could use it for leverage. But if things do turn to violence, even much later on, then the Fighter has a leg-up to Threaten the witnesses of their savagery.

To round things off there still are a few moves that are "just" useful, some in general, some mainly in combat. But now these are expected and welcome additions on top of an otherwise deep and interesting character.