Should "What is he eating? Where?" be accepted for this? It seems to make just as much sense as a translation.
As usual the whole present continuous alternate answer is not permitted even though it's technically acceptable.
Well, but in this instance the other alternative doesn't seem to make sense to me in English. "What does he eat?" implies something like "describe your entire diet."
"What does he eat?" "He likes beef and chicken, but does not eat pork or most green vegetables."
That doesn't seem to be the sense that the Vietnamese sentence implies; it seems more akin to (idiomatically):
"What is he eating [for lunch]?" "Hamburgers." "Oh, where's he going?"
It could be interpreted as simply something he usually eats at a specific place.
"Anh ấy ăn gì? Ở đâu? Anh ấy ăn phở ở quán ABC" could be interpreted as meaning:
"What does he eat? Where (does he eat that)? He eats pho at ABC"
"What is he eating? Where? He's eating pho at ABC"
I put down "What does he eat? And where?" which sounds more natural in English conversation (it sure seems implied)