This is an example of a keyword which was defined after the ability's effect had been around for a several years. Any cards which say some variation of "When this creature deals damage to a creature, destroy that creature" is now considered to have Deathtouch according to the Oracle rules text of the card.

702.2. Deathtouch

• 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 rule 510.1c-d.
• 702.2c A creature 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.

Rules Translation

• 702.2a - It is something that happens when damage is dealt, not in response to.
• 702.2b - This bypasses the need to compare damage to toughness and damage is always lethal, damage of any amount.
• 702.2c - This is the rules line that actually kills creatures with deathtouch
• 702.2d - The receiver of damage with deathtouch, but the dealer of damage is killed or removed from the game, the receiver is still killed by deathtouch.
• 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.

Reminder Text

Any amount of damage this deals to a creature is enough to destroy it.

Other Notes

• If a creature (whether it has deathtouch or not) blocks or is blocked by multiple creatures, those creatures must be put into damage assignment order during the declare blockers step. The creature then assigns its combat damage to those creatures according to the damage assignment order announced for it. It can't assign combat damage to one of those creatures unless each creature that precedes that creature in its order is assigned lethal damage. If a creature with deathtouch blocks or is blocked by multiple creatures, everything works exactly the same way with one exception: assigning even 1 of that creature's damage to a creature is considered to be lethal damage.

  Example: The damage assignment order of an attacking Acidic Slime (a 2/2 creature with deathtouch) is Spined Wurm (a 5/4 creature) then Siege Mastodon (a 3/5 creature) then Runeclaw Bear (a 2/2 creature). Acidic Slime can assign 1 damage to the Wurm and 1 damage to the Mastodon, or 2 damage to the Wurm. It can't assign damage to the Bear. Each creature Acidic Slime deals damage to is destroyed.

• If an attacking creature with deathtouch and trample becomes blocked, the attacking creature first assigns damage to the creature(s) blocking it. Once all those blocking creatures are assigned lethal damage, any remaining damage is assigned as its controller chooses among those blocking creatures and the player or planeswalker the creature is attacking. However, since the creature has deathtouch, assigning even 1 damage to a creature is considered to be lethal damage.

  Example: Yavimaya Wurm (a 6/4 creature with trample) is equipped with Gorgon Flail (an Equipment that grants the equipped creature +1/+1 and deathtouch). It attacks a player and is blocked by Siege Mastodon (a 3/5 creature). Yavimaya Wurm must assign at least 1 damage to the Mastodon. Its remaining damage may be assigned as its controller chooses between the Mastodon and the defending player. Notably, the Wurm may assign 1 damage to the Mastodon and 6 damage to the defending player. After that damage is dealt to the Mastodon, the Mastodon will be destroyed.

• If a creature with deathtouch and another creature both block or are blocked by a creature, the other creature may take into account the fact that any combat damage dealt by a creature with deathtouch is considered to be lethal damage.

  Example: An attacking Acidic Slime (a 2/2 creature with deathtouch) and an attacking Yavimaya Wurm (a 6/4 creature with trample) are both blocked by a Palace Guard (a 1/4 creature that can block any number of creatures). The Slime must assign its 2 damage to the Guard. Since the Guard is being assigned lethal damage, the Wurm's 6 damage may be assigned as its controller chooses between the Guard and the defending player. Notably, the Wurm may assign all 6 damage to the defending player. It doesn't matter which creature's damage is assigned first, as long as the final damage assignment follows all the applicable parameters.

• The rule that causes creatures dealt damage by a source with deathtouch to be destroyed applies to any damage, not just combat damage.
• A regeneration effect can save a creature that's been dealt damage by a source with deathtouch.
• If multiple state-based actions would destroy a creature at the same time (because it's been dealt lethal damage and been dealt damage by a source with deathtouch), a single regeneration effect will replace all of them and save the creature.
• If a creature is dealt damage by a source with deathtouch, it'll be destroyed as a state-based action. That means there's no time to react between the time the creature is dealt damage and the time it's destroyed. If you want to put a regeneration shield on it, or sacrifice it for some effect, or anything else, you must do so before the damage is actually dealt.
• The rules that care about deathtouch function no matter where the source with deathtouch is. In other words, if a spell or ability causes a card with deathtouch that's not on the battlefield to deal damage to a creature (like Selfless Exorcist's ability does, for example), that creature will be destroyed. This isn't the same as damage dealt by a source that has changed zones; see below.
• If a source of damage hasn't changed zones by the time that damage is dealt, its characteristics are checked to see if it has deathtouch at that time. If the source has changed zones by then, its last existence in the zone it was expected to be in is checked to see if it had deathtouch at that time.
• If an object with deathtouch gains another instance of deathtouch, the extra instance of deathtouch won't have any particular effect. If that object deals damage to a creature, a single regeneration effect will still save it.