A ranged weapon uses the Dexterity modifier for attack and damage rolls. Thus weapons in the "Melee" section become a "Ranged Weapon" if thrown (and can allow proficiency if they have the Thrown property with a listed short/long range).
See WEAPONS (PHB P.14)
- For attacks with melee weapons, use your Strength modifier for attack and damage rolls. A weapon that has the finesse property, such
as a rapier, can use your Dexterity modifier instead.
- For attacks with ranged weapons, use your Dexterity modifier for attack and damage rolls. A weapon that has the thrown property, such
as a handaxe, can use your Strength modifier instead.
Notice in the above quote "for attacks with ranged weapons" it lists handaxe (a weapon with the thrown property listed in the melee weapon section).
This is important to note as the sharpshooter feat has 3 properties. The first 2 properties talk about range weapon attack rolls and range weapon attacks. The 3rd property (and the one specifically asked about) a ranged weapon you are proficient with. Thus thrown improvised weapons (i.e. melee weapons without the thrown property) will not be valid for the 3rd property.
Not that you asked but in addition you can also use TWF (PHB P.195):
When you take the Attack action and attack with a light
melee weapon that you’re holding in one hand, you can
use a bonus action to attack with a different light melee
weapon that you’re holding in the other hand. You don’t
add your ability modifier to the damage o f the bonus
attack, unless that modifier is negative.
If either weapon has the thrown property, you
can throw the weapon, instead o f making a melee
attack with it.
Thus you can make 2 thrown attacks (Daggers) with -5 to hit +10 damage (although the off-hand does not have str/dex bonus added to damage).
Based on RAW only, there should be no confusion on this. A ranged weapon is one where you use DEX for atk/dam - says so in PHB p14 (unless it has other specific properties - i.e. "Thrown", where its still a ranged weapon but can use STR). The above question didnt ask about other DM or designers point of view, just RAW. If you hit someone with a bat its a melee weapon, if you toss the bat at someone its a range weapon. For the purpose of the feat (sharpshooter) you need proficiency as well, thus a melee weapon needs the "Thrown" property in order to become a ranged weapon and allow proficiency.