I think in informal ways it could be understood (so don´t be hard on them)
But it´s interesting to explain that it is more usual (with that structure):
What are they are having for breakfast/for dinner/for supper?
You could elaborate further, explaining that one could misunderstand (I mean the perception of ambiguity) and think that what they were eating at such meals.
To the latter - "what are they eating", to avoid ambiguity seems to memore to the point (and would be more specific in kind) - since the following question would be "what are they drinking? Or even what are they having to drink?
I mean the usual, natural way, at least for an ESL student. But I am not definite about it, others may think different or bring up more insights.
But, somehow I think a native would understand, don´t know if it sound natural.
But then, ESL-wise I would advise the "..for breakfast/dinner, etc", at least for the time being.