Both your suggestion "Bist du noch nicht weg?" and the question in the exercise "Bist du immer noch nicht weg?" are fine. The English translation is identical for both sentences.

noch = still

immer noch/noch immer = still

The "immer" is just used to intensify the "noch". It can't be translated literally into English. Maybe in spoken English, you could emphasize the word "still" to achieve a similar effect: "Are you STILL not gone?"/"Are you not gone YET?"