Not necessarily. This Vietnamese sentence is not telling anything about the newspaper (or newspapers) that the monkey is reading. It's just expressing the fact that the monkey is reading it (or them).
This could be because the specificity of said newspaper(s) is irrelevant, for example when talking about the monkey's habits. It could also be because it is clear from the context, for example if a newspaper had already been mentioned previously.
The ideal translation for the sentence would indeed be "The monkey reads newspaper", however English grammar doesn't allow that sentence. Hence, since Duolingo doesn't provide us with any context, all the following translations are valid: "The monkey reads a newspaper"; "The monkey reads the newspaper"; "The monkey reads newspapers".
As a matter of fact, the Vietnamese sentence could even be collocated in the past or in the future depending on the context, so pretty much all conjugations of the English sentence could be possible translations. However, here in Duolingo those are not accepted because, I think, they wanted to avoid creating confusion on when to use present, past or future tenses. Also it would be a monumental job adding all possible valid answers.