There are three kinds of clauses with lexical verbs in them.
Some clauses have a subject, a direct object, and an indirect object.
Three different noun phrase arguments.
- Mike told Billy the story.
Mary sent the cake to Sylvia.
These are called Bitransitive clauses.
There are not very many verbs like tell and send,
and most of them have to do with transfer.
Some clauses have a subject and a direct object, but no indirect object.
Two different noun phrase arguments.
- Mike saw Billy.
Mary hates Sylvia.
These are called Transitive clauses.
There are a lot of verbs that can occur in transitive clauses, of many different kinds.
Some clauses only have a subject, but no object of any kind.
Only one noun phrase argument.
- Mike ran yesterday.
Mary is sleeping now.
These are called Intransitive clauses.
There are a lot of verbs that can occur intransitively, too.
Frequently one verb can swing both ways.
Now, think can be transitive or intransitive. It's an active verb semantically, and always requires an agent subject; if possible, a sapient subject. I.e, human. Intransitively, it can just mean to cerebrate or vacillate, mentally or emotionally. The focus of thought is often represented with about. That's the intransitive use of think; or at least one of them.
But the presenting sentence
- Poe did not think himself a writer of inferior material.
is transitive. This use of think is equivalent to consider or believe, and means, roughly, 'to have an opinion on X as Y'. And you're correct that the predictable phrase to be has been deleted. All of these except the last one are examples of B-Raising.
- Poe did not think himself to be a writer of inferior material. (B-Raising)
- Poe did not consider himself to be a writer of inferior material. (B-Raising)
- Poe did not believe himself to be a writer of inferior material. (B-Raising)
- Poe did not have an opinion of himself as a writer of inferior material. (Not B-Raising)
Briefly, that means that the real object of think is the infinitive clause (for) Poe to be a writer...
and its Subject, Poe, gets "lifted up" and reinterpreted as the Object of think
(or believe, or consider, or any other B-Raising verb).
Since Poe is now the object of a transitive clause,
and Poe is also the (co-referential) subject of the same clause,
the rules require that the object Poe has to appear as a reflexive pronoun.
That's all. The reflexive is automatic, given that the subject and object are co-referential.