So I thought your question was interesting and I looked it up. The sources I found say it is a narrative poem, which is poetry that tells a story. Shorter narrative poems are similar in style to a short story, which why I can definitely see where your question comes from. I thought it was interesting how narrative poetry is actually considered to be one of the oldest forms of poetry, dating back to the days of Homer. Well, hope that helps... :)

Main Source: http://en.wikipedia.org/wiki/Narrative_poetry

The poem was like a short story. After reading Roosters, another poem Bishop wrote during the time she lived in Key West, I just think that this is the overall style Bishop adopts when she develops her poems. Her words are very descriptive and they can easily be transformed to a visual picture in your mind. I anticipated that she would let the fish go because she compared the hooks in his mouth to medals and a beard of wisdom. It seemed that in the instant she saw his jaw she gained respect and admiration for him.

I really liked this poem. It did seem like a short story. You can easily relate to the events within the poem if you have ever been fishing before. It was very easy to paint a visual picture of the fish from all the words she used to describe it. You can see that Bishop has respect for the fish for all it has endured.