Translation:He chose the economy as the subject of his lecture.
"as", "in the role of".
- "Mi kiel via patro diras al vi, ke ..." = "I as your father tell you that ..."
- Ni elektis lin kiel prezidenton = We elected him as (our) president
- Mi laboras kiel instruisto = I work as a teacher (or) I work like a teacher (it could mean either)
Because in the first sentence, "via patro" refers to "mi", which is in the nominative; in the second sentence, "prezidenton" refers to "lin", which is in the accusative; and "instruisto" refers to "mi", which is in the nominative.
Compare these two:
Mi elektis lin kiel prezidenton = I elected him as president = I elected him to be the new president
Mi elektis lin kiel prezidento = I as president elected him = I am the president, and in this capacity, I elected him (to some other post)
In the first case, "prezidenton" with accusative must refer to "lin" and so it's he who is the president; in the second case, "prezidento" with nominative must refer to "mi" and so it is I who is the president.
si refers to the subject so it can't be the subject itself.
There are no widely-accepted gender-neutral third person singular pronouns in Esperanto, though there are various proposals (a bit like in English).
https://eo.wikipedia.org/wiki/Seksne%C5%ADtrala_homa_triapersona_pronomo has a big list of (some of) them.