I decided to do some more research, and while I suppose you will believe this shows I am biased, I now suspect that the speaker either misspoke or the microphone didn't catch his words well.

Based on all data I have found, I think it is probable that all the NSW cases were unvaccinated (except for one case where the person had one shot of a two dose series). Here's what leads me to that conclusion:

• Only 12% of Australia has been fully vaccinated, and as of July 1st, only 6% had been fully vaccinated.
• The reports from all other countries so far have indicated that most vaccinated people have been protected against severe effects, except among the immunocompromised (transplant patients, cancer patients, etc).
• If you watch the full video from which that clip is just an excerpt, you will hear the premier of NSW imploring people to get vaccinated in order to get out of the crisis faster. It is a bit difficult to imagine such a plea immediately before an announcement that it was mostly vaccinated people that were suffering from covid there, given the relatively low vaccination rate. Here's the full video:

As an aside, it is also notable that one of the two people that died from this NSW group was a woman in her 30s with no health problems.