Q:Is Deathtouch an activated ability? Since it's a result of damage being dealt?
Short answer: No. And it’s a static ability.
702.2a Deathtouch is a static ability.
702.2b Any nonzero amount of combat damage assigned to a creature by a source with deathtouch is considered to be lethal damage, regardless of that creature’s toughness. See rules 510.1c–d.
702.2c A creature with toughness greater than 0 that’s been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action. See rule 704.
702.2d The deathtouch rules function no matter what zone an object with deathtouch deals damage from.
702.2e If an object changes zones before an effect causes it to deal damage, its last known information is used to determine whether it had deathtouch.
702.2f Multiple instances of deathtouch on the same object are redundant.