Gunslinger Headshot Ruling

Should you apply critical damage to the 10d10 damage of the following feature:

Level 20: Headshot

When you score a Critical Hit against a creature using a Ranged weapon, you can choose for it to be a Headshot. If the creature has less than 100 Hit Points, it dies. Otherwise, it takes an extra 10d10 damage of the weapon’s type.

No.

Since the ability triggers only on a Critical Hit, we must assume that the critical bonus is already factored in.

Additionally, Headshot doesn't count as part of the attack's damage in its text.

Quote from Athanar90 >>

Additionally, Headshot doesn't count as part of the attack's damage in its text.

 This is correct. The wording does not make the attack deal extra damage, the target simply takes the damage, so it is not affected by the critical hit.