They're trying to measure infection rates by analysing people who are more likely to go outside, and more likely to be infected. There's no adjustment for this confounder at all that I can see. Quick example:
Suppose there's a 10% chance of getting infected every time someone goes outside. Suppose there's a million people of which half are type-A people who go outside once this month, and half are type-B people who go outside 10 times a month.
The type-A person will have a 10% infection rate. The type-B person will have a 65% chance to be infected after a month. The average infection rate is around 42%. Yet if you randomly select someone outside, odds are 10 to 1 that it'll be a type-B person, and you'll get a far higher average of 60%, which isn't indicative of the average person, only of the average person who goes outside.
Second, the article then compares the infection rate to the mortality rate. But the mortality rate does not include excess deaths. These are quite a bit higher for NYC, about 30% or so it seems than the official figures. But even this may be undercounting (or potentially, overcounting) the impact of the corona disease itself. Other deaths might be much lower (e.g. traffic, murder) or higher (e.g. untreated cancer).
Then there's the lag-effect. There's 150 thousand confirmed infected, 15 thousand dead. But the vast majority of confirmed cases are still active, not recovered. They're confirmed because tens of thousands were hospitalised. Of the incubated people, 80% do not come out alive. There's lots of people fighting for their lives right now. Once those cases resolve, many will not have made it. And that's just hospitalised people. Then there's lots of cases who just got infected, and will be developing symptoms in 1-2 weeks.
The way exponentials work is that lag is way more important. In the first weeks NY doubled every 2 days. That means if you have 10 thousand today infected today, in 10 days that's 320 thousand. That's when people start to get symptoms, and 10 days later people start dying from the symptoms. That means your infection count can go into the hundreds of thousands or even millions before seeing any death. But you can't conclude mortality figures from that, at all.
In short, the 21% and the 0.5% conclusions are extremely premature and should not be reported like this. It's good to report the measurements, in context, but you can't draw the conclusions about the population or disease from it.