I think you wouled not be asking this if your work visa had already been issued. That means the business has not sponsored you yet. In NZ you are able to transfer your work visa to another employer easily by applying to immigration.
I think your main issue is not that they moved but that your visa has not been issued. Once you have a work visa and you arrive in NZ you are able to change the employer as long as you keep the requirements of your visa such as essential skills category and the new employer is an accredited employer