The ranger’s class feature grants Two-Weapon Fighting, and meets that prereq
Two-Weapon Defense requires two things: the Two-Weapon Fighting feat, and Dexterity 15.
Taking the English translation as authoritative (since the original authors were working in English), the ranger class allows you to get the Two-Weapon Fighting feat as a bonus feat, that is, you actually get the feat. It has never been otherwise in any English edition of the book; the wording in French is purely an issue of translation.
Furthermore, the ranger allows you to get the feat even if you do not meet its requirement: Dexterity 15, but restricts the armor you can use at the same time.
However, the ranger class does not waive the Dexterity 15 requirement of Two-Weapon Defense. Thus, if you are a ranger with Dexterity less than 15, you do not qualify for Two-Weapon Defense: you have Two-Weapon Fighting, but not Dexterity 15, and Two-Weapon Defense requires you to have both.
Moreover, if you do have Dexterity 15, and you take Two-Weapon Defense, it effectively inherits the armor restriction of the ranger’s Two-Weapon Fighting. Because wearing heavier armor means you lose Two-Weapon Fighting, you would lose the requirement for Two-Weapon Defense and thus be unable to use it. Probably won’t come up, unless someone forces you to wear armor somehow, but worth knowing.
As a complete aside, it may be worth pointing out that Two-Weapon Defense is an awful feat, and not worth taking. Shield bonuses to AC don’t apply to touch AC, only to regular (armored) AC, and that is not very valuable at all. Even if it was, +1 is a tiny bonus. Not in any way worth a feat.
Versatile weapons cannot work with this feat.
There have been no errata to re-word the feat itself.
Flavor-wise, the feat only makes sense with big and heavy weapons.
You’ve learned to put the weight of a weapon to your
advantage, letting its momentum empower your strikes.
Rules-wise, the definition is perfectly clear.
Before you make a melee attack with a heavy weapon
that you are proficient with, you can choose to take a
-5 penalty to the attack roll. If the attack hits, you add
+10 to the attack's damage.
The feat is targeted at only STR-based characters, using both hands (as all Heavy weapons have the two-handed property). It is too flexible to be used with versatile weapons. Consider that you could drop something from your hand (like an Arcane Focus, or something else), attack with both hands, and pick the thing back up with your free-object interaction. This is even more imbalanced when characters have multiple attacks, advantage, and/or extra turns or abilities.
Eldritch Fighters could use their Action Surge to either attack several more times and re-equip the Arcane Focus for a War Caster AoO.
Multi-classing into Rogue-3 makes you able to use Fast Hands to equip a shield as a bonus action, so allowing you to have +2 Armor when your turn was done.
But maybe the most broken combo here would be Monks. Dexterity monks could now use a 2-handed DEX Quarterstaff with -5/+10 along with their unarmed strikes.
Any character with Haste (+2 AC, and an additional action)
I'm sure there are other cheesey combos out there that could be abused.
Consider also that you could now use this with weapons like the Quarterstaff, Trident, or Spear, which only do 1d8 damage (when used with both hands). Getting a +10 damage on a weapon whose maximum damage is 8 is a lot more valuable than with a weapon whose maximum damage is 10 to 12.
As a house-rule, I would not allow it. I very much enjoy the flavor, and the limitation, of the feat, requiring a big and heavy weapon to be used. My players are also power-gamers - I'm sure they'd exploit this somehow. When fighters and barbarians can pull off several attacks per turn with advantage, this becomes quite imbalanced compared with casters or ranged characters.
Best Answer
Your PHB is correct: Weapon Master does not grant you a fighting style
The Weapon Master feat (PHB, p. 170) grants you:
There's no mention of acquiring a fighting style. Modifying the feat to include one would be introducing homebrew to your game.
No other official feats currently allow a PC to learn a fighting style, either.
Note: One possible source of your confusion (suggested by linksassin in the comments) could be the similarly named Great Weapon Master feat (PHB, p. 167) - which is different from the Weapon Master feat, but also doesn't grant a fighting style - and the name of the Great Weapon Fighting fighting style.
The Great Weapon Master feat and the Great Weapon Fighting fighting style work well together for obvious reasons. There is no overlap in the benefits they provide.