What a misleading title and story.
The airport is not closed as you can easily see on any tracking website. It was never closed.
There was a ground stop in place. That means no new flights were allowed to take off with destination LGA.
The ground stop has since been lifted and the rate limited to 30. (Which is basically the standard rate if there is some unvaforable winds, basically every 3rd day)
Also there have been rate reductions in the New York area without any shutdowns. They are understaffed and it is prime season for colds with sore throats.
The facility was understaffed before because they do quite a bit of vectoring in complicated airspace so it's hard to get new trainees, at least that's what i read somewhere.
Not saying that the shutdown is not contributing to the staffing shortage but just assuming the staffing shortage is because of the shutdown is just crazy.
Anyway great reporting by BBC there, so accurate and not jumping to any conclusions at all.