That's interesting but I have often heard people ask "what height is he?" especially when asking the height of a smaller person, where the adjective "tall" somehow doesn't seem appropriate, the question "how short is he?" wouldn't seem right either.
Think about it: you probably wouldn't ask how tall was something quite short or low, but you might ask the height of it.
It would depend on the information that the inquirer is requesting...
1. How is his height?
This could be seen as if you were asking of the person's health, and could probably get you an answer of it's doing well or not so well. Not what you really wanted to know.
2. What is his height?
This question would give you the the person in question's height if known t