In my opinion, "died" here cannot be considered as a linking verb, because "die" implies a kind of a action, that is the very act of dying. It is an intransitiv verb. Yor sentence could as well read simply "He died," with a complete meaning.
If you want a linking verb, you could say:
"He is young" or "He seems young".
So I can't see "die" in your example as a linking verb, nor can I think about any other example where "die" could do a linking verb job.
PS Not a native speaker (neither grammarian nor linguistic)