For the Korean boy band BTS, the success of its sprawling, genre-defying pop album “Map of the Soul: 7” is a sign of how the rising K-Pop act is cementing its place in American culture.

This past weekend, the album—which mixes rap, ballads and electro-pop—hit No. 1 in the U.S. on the Billboard 200 chart, the band’s fourth chart-topper in roughly a year and nine months.

It’s...