For non-defining clauses two possibilities are :
a) a quiz - Stage 1 : start by giving them a short five item quiz with items like : Can you name the person who discovered penicillin? What do you call the famous statue which is on an island in the sea near New York? Can you name three animals which only live in Australia?
etc. Divide them into teams and give one point for each right answer. Stage 2 : Each team then has to write three (or more) similar questions to ask the other groups. They must know the answer to their own questions - if you let them prepare for homework they can consult reference books. They then ask the other teams their questions - again one point for each right answer, but if they come up with a question that no-one can answer, then they get the point. At the end, the team with most points wins.
b) A circumlocution strategies game. See here.
Non- defining relative clauses are mainly a feature of written language, and it's therefore more difficult to come up with something fun.