They Knew What They Wanted was written in the 20s. Now I know that for songs, contemporary applies to anything after the 60s, but as far as plays go… Classical seems to define Shakespeare or Ancient Greek Theatre. Are plays written in the 1920s considered contemporary or classical?
Usually, what they mean by classical is heightened language, preferably verse. The safest bet is to do Shakespeare. I haven’t read “They Knew What They Wanted”, but regardless of when it was written, it can be considered contemporary for auditioning purposes if the language is more colloquial. Some playwrights are kind of in between, like Shaw, so they are best avoided when asked for two contrasting pieces.