"아이들이 시끄럽게 놀아요."
Translation:The children play noisily.
It does not accept 'Children play noisily' prefering 'The children play noisily.' However, 'the' in Korean is '그' is not in the sentence
I would completely agree if they used 아이는. But this sentence uses 아이들이, which is using children in plural form 들 and specifying them as a subject rather than a topic with 이. So the sentence is referring to a particular group of children, hence "the children" instead of "children" in general.