By this definition, a thrown weapon is a ranged weapon because it is used to attack a target at a distance.
It says they are classified in the table as either melee or ranged. Which makes sense for organizing them and displaying them. But if you assume the second sentence is a rule independent of the table, it means that any weapon used at range is a "Ranged Weapon".
No a thrown melee weapon is still a melee weapon, a thrown ranged weapon is a ranged weapon.
Properties like thrown or reach might change the fact that a weapon can be used at a distance greater than 5' but neither changes the weapon type. By your logic a whip, halberd, or lance is a ranged weapon. A dagger is a melee weapon with a property called thrown, a dart is a ranged weapon with a property called thrown.
How do we know that? Couldn't the PHB be written by multiple authors, one of which used "Ranged Weapons" while another one used "Ranged Weapon Attacks" even though they both meant the same thing and the editors assumed they meant the same thing? Besides, how do we know that "Ranged Weapon Attacks" include include thrown weapons? Wouldn't the definition of a "Ranged Weapon Attack" be an attack with a "Ranged Weapon"? If "Ranged Weapons" are only things that are under the "Ranged Weapon" category in the equipment section that would imply that "Ranged Weapon Attacks" only work with bows and the like.
RANGED ATTACKS: When you make a ranged attack, you fire a bow or a crossbow, hurl a handaxe, or otherwise send projectiles to strike a foe at a distance. A monster might shoot spines from its tail. Many spells also involve making a ranged attack.
There are three types of ranged attacks mentioned throughout the books. The broad ranged attack, the ranged spell attack, and the ranged weapon attack. Those are different types of attacks, and have nothing to do with different types of weapons.
It seems unlikely that they'd make a feat and make it only partially effective if you are using thrown weapons. The feat is then a trap if you are throwing weapons. They said they were trying to avoid traps.
There are other feats that work only partialy depending on what weapon you are using, the first part of great weapon master for example works with any melee weapon, that means it works with rapiers and daggers. The second part only works with melee weapons that are "heavy", doesn't make the feat a trap choice.
Plus, there doesn't appear to be any balance issues with allowing thrown weapons in these situations. It seems like restricting things like to restrict things.
That is a debate point for discussing RAI or rules in play at the table, not the rules as written.