The 1999 Seattle concert was part of Metallica's "Garage Inc." tour, a series of concerts where the band covered songs by other artists. "Nothing Else Matters" was one of the covers performed during this concert, along with other notable songs such as "Astronomy" by Blue Öyster Cult, "Turn the Page" by Bob Seger, and "Whiskey in the Jar" by traditional Irish music.
Metallica's cover of "Nothing Else Matter" was not specifically selected as a tribute to Kurt Cobain, but rather as part of the overall theme of paying homage to other musicians and their work. It is worth noting that the band has performed this cover on various occasions throughout their career, as a way of showing appreciation for other artists and diversifying their concert setlist.
While it is understandable to associate the performance of "Nothing Else Matters" with Cobain's death due to the somber tone of the song and the location of the concert in Seattle, where Cobain was based, the band's motivation behind the cover was not directly related to this tragic event.