Does a legendary creature dying trigger abilities that watch for creatures going to the graveyard?

A legendary creature is simply a creature with the supertype "Legendary." The supertype grants special rules (the Legend Rule, CR 704.5j), but it does not change the fact that the card is a creature permanent on the battlefield. When it dies — meaning it moves from the battlefield to the graveyard (CR 700.4) — it satisfies any trigger condition that watches for a creature dying.

Triggered abilities use the last-known information about the permanent as it existed on the battlefield to determine whether trigger conditions are met (CR 603.6). So when a legendary creature dies, the game looks back and confirms it was indeed a creature, satisfying triggers like "Whenever a creature dies..."

This also applies regardless of why the creature died — combat damage, a destroy effect, lethal damage, or the Legend Rule itself (which is a state-based action sending it to the graveyard, CR 704.5j). All of these count as dying and will trigger relevant abilities.

Concrete example: You control Zulaport Cutthroat ("Whenever a creature you control dies, each opponent loses 1 life") and your legendary Thalia, Guardian of Thraben dies in combat. Zulaport Cutthroat's ability triggers because Thalia was a creature you controlled when she went to the graveyard from the battlefield.