looking or looking like?

I am a Korean English teacher.
I have encountered a strange sentence like the following.
In the first sentence, “looking” should be changed into “looking like”, shouldn’t it?, for the word “look” is an intransitive verb. Please help me to teach correct English, will you?
If it is grammatically correct or incorrect, would you explain why?
But when I came downstairs, he was dressed, sitting by the fire, looking a very sick and miserable boy of nine years. When I put my hand on his forehead, I knew he had a fever.