The New World Clubcard is a fully functioning Flybuys card that can be used at other retailers, according to this FAQ on the flybuys website.
How confusing can things get.. You can only use it if you're crediting to Fly Buys though - not Airpoints. What happens with your Airpoints accruing New World card if you change the earn to Fly Buys with New World? Will the same number then work for Fly Buys? I'd doubt it.