clearstream
(He, Him)
Together with @Maxperson's excerpt from DMG text this seems like a fair reading to me, i.e. destroyed is synonymous with killed but broadened as you say to account for things that aren't alive in the first place. ThusI'd say it's more a catch-all term intended to include undead, constructs, and the like which aren't "killed" on losing their one hit point as they're not alive to begin with. Having to say "killed or destroyed" every time would get awkward.
A minion is destroyed when it takes any amount of damage.
includes
A minion is killed when it takes any amount of damage.