Path of the Slayer
Dwarves who have been disgraced, crossed in love, or otherwise humiliated abandon traditional society and seek the sweet release of death. They hunt the most dangerous of monsters in the hopes of finding a glorious end.

Restriction: Dwarves Only
Only dwarves can follow the Path of the Slayer. The cult of the Slayers is esoteric and strange, the oaths they take incomprehensible to any without the dwarves' obsession with honor.
Your DM can lift this restriction to better suit the campaign. The restriction exists for the Old World of Warhammer. It might not apply to your DM's setting or your DM's version of the Old World.
It makes sense given the background, however I personally like the idea of an ethos being able to be embraced by any race so my personal preference is the broader one.

Lost Proficiencies
Starting when you choose this path at 3rd level, you lose proficiency with medium armor and shields.
Ew. Losing proficiency is a bit weird. You could just go down the monk route of adding "whist not wearing medium or heavy armour and whilst not wearing a shield..." to abilities to soft enforce this, or more appropriately barbarian. Also, losing proficiency would let you do something like dip a level of another class to get it back, which migh be unintended.



Fighting Style
When you choose this path at 3rd level, you adopt a particular style of fighting as your specialty. Choose one of the following options. You can't take a Fighting Style option more than once, even if you later get to choose again.
Great Weapon Fighting. When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll, even if the new roll is a 1 or a 2. The weapon must have the two-handed or versatile property for you to gain this benefit.
Two-Weapon Fighting. When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack.
Generally not great fighting styles, so not a powerful ability - but its thematic and not alone...


Slayer's Quarry
You have sworn to destroy an enemy of your race...or die trying.
At 3rd level, you choose a type of creature: aberrations, beasts, celestials, constructs, dragons, elementals, fey, fiends, giants, monstrosities, oozes, plants, or undead. Alternatively, you can select two races of humanoid (such as gnolls and orcs) as your quarry.
You have advantage on Wisdom (Survival) checks to track your Slayer's Quarry, as well as on Intelligence checks to recall information about them.
You choose one additional type of quarry at 10th and 14th level. As you gain levels, your choices should push you toward ever greater opponents—adversaries who may grant you the end you seek, or whose own defeat might be worthy of a song.
So I see why this is this way, but if the PHB ranger has taught us anything its that people tend to not like the enemy dependant abilities. Having broader classes of enemy might be better - bonuses against large or larger enemies, or spellcasters etc.. Honestly, I feel level 3 could use a bit of extra support.

Now I don't have a problem with this being different, but I think all Barbarian subclasses have a "whilst raging" ability that gives an extra imact to their rage.



Stout-hearted
The quest for glorious death is all that sustains you now, and nothing will stand in the way of your destiny.
Starting at 6th level, you have advantage on saving throws against being charmed, frightened, or possessed, and you cannot be charmed, frightened, or possessed by your Slayer's Quarry.
The situational thing comes back again... Its thematic, again. It kind of works as it isn't tied to rage but seems less significant than the frenzy barbarian whilst also being less flexible. Still level 6 barbarian abilities are not always the best.


Grudgelord
When you meet a foe you have vowed to kill, only one of you will walk away alive.
Starting at 10th level, while you're raging, hostile creatures within 30 ft of you have disadvantage on attack rolls against creatures other than you.
While you are within 30 ft of your Slayer's Quarry, you have disadvantage on attack rolls against creatures other than your quarry, and you must succeed on a Wisdom saving throw in order to move more than 30 ft away from your quarry. While you're raging, any of your Slayer's Quarry must make the same save to move more than 30 ft away from you. The DC for this saving throw is equal to 8 + your proficiency bonus + your Constitution modifier.
So a nice tanking ability... but on a barbarian subclass that gets no benefits to resiliance in the subclass. It seems to overlap too much with the ancestral guardian abilities as well - kind of trampling all over them.

Mighty Blow
You have become an avatar of doom, and those foolish enough to stray into your path do not often live long enough to regret their mistake.
Starting at 14th level, any melee attack roll you make while raging is a critical hit on a roll of 19 or 20, and your Rage Damage bonus is doubled against your Slayer's Quarry.
Yes... its OK. It feels like more damage is a bit bland, especially this late on in the game. On the other hand it is quite a lot of extra damage.




I wonder if you could do something like move some of the capstone to 3rd level? Something like "when you enter a rage you may swear an oath of destruction against one creaure you see. Whilst raging an unmodified roll of a 19 or 20 is a critical hit. At level 10 this increases to 18, 19 or 20. Something to help you chew through the big HP of empting enemies and that would really encourage you to reckless attack?