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.