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.
A disintegrated creature and everything it is wearing and carrying, except magic items, are reduced to a pile of fine gray dust. The creature can be restored to life only by means of a true resurrection or a wish spell.
Why would you need to be "restored to life" if you weren't dead?
I see no flaw in this argument. Instead of dying, the character exists like the guy from “One” by Metallica, desperately waiting for a stiff breeze to end his existence.
The spell specifies you turn into gray dust. Unfortunately gray dust has no listed stat block.
Luckily it is mentioned in "Tales from the Yawning Portal", "The floor of this room is covered with a layer of fine gray dust and ash, three inches deep."
Based on the rest of the description you are restricted to the room in which you turned to dust and the only action you may take is casting " Minor Illusion", with the added restriction of all illusions must be humanoid.
You're not dead when you're petrified, either, which can lead to some pretty interesting exploits, rules-as-written.
Petrified creatures count as creatures, not objects, so rules-as-written you can determine if a statue is a petrified creature by trying to target it with a spell that requires a creature for a target.
With the cantrip Poison Spray, you can check for petrified creatures without using spell slots or risking damaging the creature, since it would be immune to poison while petrified.
Why would it matter if it says you die? It's not like there's a rule that dead characters can't take actions. Or that they transform into objects. Or get sent to another plane of existence depending on who they worship and their alignment while leaving an object behind.
I'd like to imagine that this is how non-necromantic sapient undead creatures are created, someone has all their flesh incinerated away but somehow their soul clings to the bones, and bam sapient skeleton.
In this case it could result in a poltergeist, which uses the dust to interact with things.
The rules also don't state that being incapacitated impairs movement in any way, dropping to 0hp is stated to incapacitate you. So you can just move away at 0hp.
Obviously we have DMs who aren't robots and will play to the spirit of the game, not the word of the rules.