With any review like this there will always be a few mistakes, which I hope they correct. But I think this basically makes sense.
There are many reasons for the closings. The priest shortage is mentioned. But several other factors are probably more important. One is the disappearance of the old ethnic neighborhoods. Little Italy has gotten smaller. Little Germany has virtually disappeared. There are more blacks and fewer Catholic ethnics. Most of the Irish and Italians have moved to the suburbs.
A lot of young blacks like the kid in the picture have profited from going to Catholic parochial schools. But they are not Catholic themselves, and somebody has to pay for these schools. The NY state teachers unions have been especially vehement against any kind of voucher system, and the liberal judges have frequently shot them down. Same with the hospitals. Catholic schools and hospitals are serving mainly non-Catholics, and that can't continue unless somebody is willing to pay for it.
There are plenty of thriving Catholic churches in NYC. I attended Our Lady of Victories church down on Wall Street, and it was great. But other churches are nearly empty and simply don't support themselves--maintenance, heating bills, and all the rest of it.
As you pointed out, the first catholic settlers lived in 'ethnic' neighborhoods and built their churches to resemble those they left behind. It is not unusual in the northeast, to find several catholic churches within blocks of each other, simply because one was built by the Irish, another by the Italians and yet another by the Poles.
This is also true in the Eastern Churches where their 'ethnic' neighborhoods have also disbanded, though not to the extent of their Latin counterparts. The ongoing persecution of christians in the Near East ensures a constant flow of eastern christians to the west. Here they seek comfort and solace in 'their' catholic churches, to which RCs are also being drawn for the beauty and reverence of their liturgies.
As my pastor recently commented: The Eastern Churches are the same faith, just a different flavor.
Interesting statistic is that the largest concentration of Italian immigrants (aka REAL Italians) in New York is on the Upper East Side. These tend to be wealthy folks in the arts and finance, many of whom are part of the jet set.