I'm afraid you have misunderstood this sentence. "In the interim" means "in the meantime", that is, in the time between now and when processing of your residence application finishes. They are not talking about the Interim Visa here - it just happens to use that same word in its name.
Yes, you have to get new work visas. Quite likely, you will not need to provide new medical certificates, if it is less than 36 months since you supplied them before. A4.25 c here.
https://www.immigration.govt.nz/opsm....htm?35154.htm
Don't worry that time is short until your existing visas run out - as long as you lodge the new applications while the old ones are still running, then at that point, INZ can issue interim visas to keep you legally in NZ while waiting for processing to be done.