West Side Story is a musical play with a story by Arthur Laurents, music by Leonard Bernstein, and songs by Stephen Sondheim. It is a modern adaptation of William Shakespeare's play Romeo and Juliet, set in New York City in the mid-1950s. The two young lovers are from different ethnic groups and reflect the ethnic tensions in New York in the mid-twentieth century.
The play is not a tragedy in the classical sense. It does not address the inevitable downfall of a noble person who has a "tragic flaw" or makes a flawed decision in a situation from which there is no possible escape. Although the plot does touch on racial tensions between gangs, the characters are not the powerful nobles or royalty of tragedy whose acts influence the fates of cities or kingdoms. Instead, it is a modern romantic drama in which two young lovers die. The ending is sad and evokes pity in the audience.
Thus while one can apply the term "tragic" in the popular sense of "having an unhappy ending" to the play because characters with whom the audience sympathizes die, the plot and other elements of the play do not really fit into the dramatic genre of tragedy.