(That link only covers through 2019, but if you look at the official CompStat data the two year trend for 2019–2021 is also negative: https://www1.nyc.gov/assets/nypd/downloads/pdf/crime_statist...)
Some crimes are down, some (e.g. murder) are up.
Crime is down overall, and I suspect that if you controlled for the murder rate increase in all US cities over the past two years it might be flat or down in NYC as well.
For example, as of 2017 feeding pigeons was a misdemeanor in Las Vegas [1]. That will show up in crime data, but you'd be hard-pressed to convince me that it correlates with the murder rate. And if you wanted me to compile a report on crime data, I'd probably ignore it altogether (which is essentially what people are doing when they refer to "violent crime" states).
For a slightly more charged example, let's say property owners push a law against sleeping in public. If they succeed and police don't enforce it, are they "gaming" the metrics? What if most other locals actually oppose the law?
[1] https://www.latimes.com/nation/la-na-illegal-pigeon-vegas-20...