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.
20I'd be surprised if there's any language where it's ungrammatical to be redundant. – Matt Samuel – 2020-05-04T00:10:22.163
3All the answers so far assume “theaters” refers to cinemas or stage-houses. Without context, I read this with the much broader meaning: a theater is a specific place or context where things happen, like restaurants, parks, hospitals, etc. – Dúthomhas – 2020-05-04T01:44:45.307
I think it's fair to say that since there is no Academy of the English Language (or other final arbiter beyond usage), that usage is allowed, and even not all that problematic. Obviously some patterns are clearer than others, and I would never have used it that way. Instead, I would have written it something like this "COVID-19 plagued New York City, especially its many theaters" or something of that kind. – None – 2020-05-04T02:39:11.747
2Colorless green ideas sleep furiously – Jack M – 2020-05-04T06:33:45.333
13You seem to have some good answers to the question you thought you were asking already, so I won't add another one. But technically speaking, I think the answer should be: "grammar doesn't have anything to say about this".The sentence "snow flakes are white flakes of snow and they reflect all light" has a lot of redundancy in it but there is no grammatical problem with it. Just like the sentence: "horses are blue spheres of wood and they float in the air" which has pretty much the same structure. The content of the sentence is false, but it is equally valid in terms of grammar. – CompuChip – 2020-05-04T07:20:52.753
This isn't technically redundant. – Panzercrisis – 2020-05-04T21:39:35.423
4There's a big difference between a grammatical mistake and a logical one. If a language disallowed illogical statements, then it would not express the full range of human conversation. – jpaugh – 2020-05-05T06:44:36.870
Redundant information breaks Grice’s maxims - for example “asbestos free cereal”. https://xkcd.com/641/ https://youtu.be/IJEaMtNN_dM
– Tim – 2020-05-05T17:11:41.777