INZ are not concerned unless an offence has been committed, one of those on the list at that link.
Demerit points on your driving licence are nothing to do with immigration.
However, be warned. The NZ police are very strict on traffic law. This first time, you got a roadside fine. If you are caught breaking the law in your car again, the system would show you have had this previous infringement, and that other time, you would get a court summons, a more serious punishment, and start to build a police record. That CAN be a hindrance for getting later visas.