Activated ability

[The Original V]

Is annihlator an activated ability because it is used when the creature attacks causing the ability to activated.

[Gorzo]

Annihilator is a triggered ability, not an activated ability.

Activated abilities can be spotted by:
cost:effect (note the colon)

Triggered abilities can be spotted by:
If/when this(trigger), do that(effect).

Because annihilator is "when this creature attacks (trigger), defending player sacrifices X permanents (effect)," annihilator falls under the triggered ability category.  Things that block activated abilities like {Pithing needle} will not stop annihilator.