Did you vever fill a glass with water and ice? When the ice melted did the glass “overflow”? No of course not.. the displacement by the ice was equal to the fluid amount.. It is no difference with the glaciers...So even IF they really did melt, NYC is safe
Your illustration doesn't hold up for glaciers or for Antarctica. When the ice starts on land and then melts or breaks off into the sea, it will cause a rise in sea level, much the same as if you take a full glass of water and add an ice cube to it. It will overflow.