Yes, they are. They count anyone admitted to a hospital in NYC, at any time, for any duration:

https://github.com/nychealth/coronavirus-data/blob/ced762b25...

> Hospitalization counts reflect the total number of people with COVID-19 ever admitted to a hospital, not the number of people currently admitted.

If you go to the ER and make it to a treatment area, you're admitted. These are bright-line distinctions. Nobody is making judgment calls on the data ("did this person really get admitted, or is it just someone in the ER for an hour? Let me look at the chart!") at this level of analysis.