You have said it correctly.
Merry and
Eowyn "wound" the
Witch-King.
Hear what is said:
"So passed the
sword of the Barrow-downs, work of
Westernesse. But glad would he have been to know its fate who wrought it slowly long ago in the
North-kingdom when the Dúnedain were young, and chief among their foes was the dread
realm of
Angmar and its sorcerer king. No other blade, not though mightier hands had wielded it,
would have dealt that foe a wound so bitter, cleaving the undead flesh, breaking the spell that knit his unseen sinews to his will.
It is not said he was 'killed'. The great likelihood... he was simply undone, similar to
Sauron and
Melkor. His 'spell' was broken.
That said, he WAS a human, whose blessing is to die eventually. Ent is uncertain when and how that happens... something has been said about the
spirits of man too going to the
Halls of Mandos until the time of renewal, or such things.
The Witch King was man, not
Maia or
Elf, endowed with the same 'life' they were. Ent needs to leave the full details of this part to others whose knowledge far exceeds his.