If you restructure the sentences to get rid of the modifier clauses, the sentences would be:
1) The chicken soup eats the child. That soup is spicy. 2) The child is eating the chicken soup. That child is spicy.
Both sentences are really weird. 1) Soup doesn't normally eat anything, let alone children, and 2) children aren't spicy (I assume - I've never eated one, lmao). The correct answer, which makes a lot more sense, would be reworded as "The child is eating the chicken soup. That soup is spicy."
So in these sorts of sentences, do you need to put the subject (chicken soup) right next to the verb? Seeing the answer makes me understand the child is not the subject, but part of an adjective phrase (if that's a proper grammatical term). But before seeing the answer, it is a difficult sentence to understand.
because in your sentence,
""The child eats spicy chicken soup" "
the verb is [eats], and "the child" is the subject.
But in this sentence,
"아이가 먹는 닭고기 수프는 매워요."
[매워요.] is the verb, or really, adjective/state of being. And the topic is the chicken soup.
The child eats spicy chicken soup would be 아이가 매운닭고기 수프를 먹어요.
It makes sense, but it doesn't fit the structure of the sentence. The primary verb in the sentence is 매워요 (is spicy), so an accurate translation should be "(something) is spicy." The something in this case is the chicken soup, 닭고기 수프는. The other words are just modifiers to the chicken soup: it's eaten by the child (아이가 벅는).
Thus we get the Duo translation, with the adjective phrase in parentheses: "the chicken soup (that the child eats) is spicy." In my opinion, notstarboard's translation of "The (child-eaten) chicken soup is spicy" is quite helpful, because it preserves the sentence structure (at the expense of sounding a bit awkward in English).