The numbers you've seen are probably deaths of infected people not the entire population.
No, I just slightly misread OP’s confusingly worded stat. Base deaths in NYC is around 6k/month. Covid-19 deaths alone have been way above that number. Numbers are obviously not in for the month of April yet, but it’s looking more like it’ll be closer to 30k deaths in NYC per CDC[0]. So that’s 24k more deaths per month, aka 5x (where my several orders of magnitude came from). If you use the scale OP used, that’s about .3% of NYC population in excess deaths, so one order of magnitude higher.
[0] it’s at 26k right now with a bit under a week left - https://www.cdc.gov/nchs/nvss/vsrr/covid19/index.htm