There are a few things to consider here.
Firstly, grammar doesn't generally concern itself with the meaning of a sentence. There is a famous example by Noam Chomsky of a sentence which is grammatically correct, but nonetheless nonsensical in multiple ways: colorless green ideas sleep furiously. So the sentence you give is grammatically correct because it is of the form "[noun phrase] plagued [noun phrase] and [noun phrase]", which is allowed by the grammar of English.
Secondly, being redundant doesn't make something nonsensical. Nonsense would imply that the two parts of the sentence contradict each other, not just that one of them was unnecessary. So the sentence is not nonsensical either.
Thirdly, if a sentence is technically redundant, that doesn't necessarily mean it is bad style. Repetition and redundancy are often used as literary or rhetorical devices, e.g. to emphasise a point. In this example, it is used to establish context, first to the city, and then to "zoom in" to the city's theaters.
Finally, it's worth knowing that the specific structure used in this example, "X and its Y", is very common, and "[city] and its many [item]s" is almost a cliché in its own right.