If you just say, "COVID-19 plagued New York City," then maybe all the theaters were okay. (It's extremely unlikely, but possible.) Maybe they were okay, and maybe they were plagued. That sentence doesn't tell you. It just tells you that the city was plagued, but it doesn't tell you which part or parts of the city.
However if you say, "COVID-19 plagued New York City and its many theaters," then theaters definitely were plagued.
However, let's look at another sentence:
The theaters in New York City were plagued, and in New York City, the theaters were plagued.
This sentence is bad style. It is very redundant. It sounds kind of stupid. However English grammar does allow this. It is not a grammatical problem, but a problem with style.