Romantic music has melodies with tenderness and a quality of longing that match the Romantic quality of poetry that they set.
Erlking in particular conjures the images described in the story it captures the strangeness and wonder of Goethe's celebrated balad, whatever is described in the poem is shown through the music, as a result the music follows the narrative and builds us up to the end where the last line "in his arms the child... was dead"
Romantic music generally refers to a style and time period of music composition that ran from about the early 1800s to around the end of that century. This period followed a "classical period" where classical composers went from a more strict, templated style of composition to a more dynamic, emotional style. While the piece is not "romantic" by our current dictionary definition of love, etc, it is romantic in that is emotional and has a wide dynamic range.
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