a literary magazine’s new writers’ award

[suprunp]

It’s very unusual for a seventeen-year-old girl to win a literary magazine’s new writers’ award.
(H. Murakami; 1Q84)

Would you be so kind to expand on why it is 'a literary magazine'. Is this because there wasn't only one concrete literary magazine that organized the competition, but rather this competition encircled the whole industry, so to say?

Thanks.

[5jj]

My understanding is that there might well be several literary magazines giving awards to new writers. Each one of these could be described as 'a literary magazine's new writers' award'.