Disclaimer: this is purposefully obtuse.
Other effects in the game which explicitly state they kill you:
Shadows, succubi, massive damage, death saving throws, beholder death ray (notably not even their disintegration ray kills you), power word kill, vampires, mind flayers, night hags, drow inquisitors.
Clearly, if they intended for disintegration to kill you, they'd have said so. Since specific overrides general, and there is no general rule that disintegrated creatures are dead, I rest my case. QED.
It doesn't kill you, it turns you into an inanimate object.
Edit: And objects aren't creatures.
Spells do what they say they do, and disintegrate doesn't change you into an object. Compare to True Polymorph, a higher level spell, which can creatures into objects.
I agree that "spells do what they say" but a pile of dust is definitely an object, not a creature. That said, I'm willing to concede that it doesn't turn you into a object because it says one of the only ways to be restored to life is through True Resurrection which targets creatures. (And I don't feel like being so obtuse as to argue that the specific rule of Disintegrate saying True Resurrection allows the dust to return to life means it overrides the general rule of True Resurrection targeting creatures lol.)