Hola Abbie

Relative "que" us used to refer to things and people, while relative "quien" is only used to refer to people. In the text, "que" is being used first in a defining clause:

Miguel Hernández was a wonderful Spanish poet who wrote "Elegy" in 1936, ...

We can't use quien here. (see explanation a bit later)

And then "quien" is being used later in a non-defining clause (because quien, quienes are not used in defining clauses unless the relatvie is preceded by a preposition):

... to the memory of his friend Ramón Sijé, who had passed away a year earlier.

You can see a "comma" used here, before the relative. This is necessary when it is a non-defining clause. In this second sentence, we could have used "que" as well. The use of "quien" makes it more formal, and tends to be used in formal texts, more than in everyday conversations. 

To learn more about defining and non-defining clauses in Spanish, here is a Kwiziq article where you can find all the information necessary and lots of examples. 

I hope it helps. 

Saludos cordiales

Inma