It was posted on https://www.labor.ny.gov/home/ last week, that they waived the waiting period. I don't see that now but it does say
I think you're confusing the waiting week with minimal employment requirements.
The waiting week was waived by NY at the start of the crisis, and then instituted by the Fed as part of the CARES Act.
The minimum employment requirements still stand for State Unemployment Benefits, but everyone who doesn't qualify under the State because of that is eligible for Pandemic Unemployment Assistance, as part of the CARES Act. This is administered by the State as well, and in NY now has the same process as a regular unemployment claim. The amount you'll receive depends on several factors, but it'll always be augmented by $600/week from the Fed (no separate application or process needed. It's automatic).