Ihm ist nicht gut
I don't understand why the two correct answers are: "He isn't ill" and "He is not well". The "He isn't ill" don't seems to make sense...
"ihm ist nicht gut" belongs to quite a family of phrases. All of them voicing a sensation. "Mir ist heiß", "mir ist kalt", mir ist schlecht""I am hot (literally), I am cold/freezing, I am unwell/ill/sick. The translation "he isn't ill" is definitely wrong.
It looks like an error since he can't be "not ill" and "not well" at the same time. If you happen upon the sentence again, report it using the link at the bottom left of the page. It should say, "do you still think you're right? Let us know." or something to that effect.