I had it originally without the the but added it because in the past I
always got burnt by not including it!
Also, what if you are having a discussion about an event like The Esperanto Congress, which takes course over several days and make reference to the first day and want to know what was served at that first breakfast- is it not acceptable to say, "What do(did) you eat for the breakfast?"
I think the "la" makes sense if you look at the word "matenmanĝo" which, when deconstructed it reads "morning meal". So the sentence is just asking what you had for "the morning meal" in which case we already have the word breakfast. Other languages may not, so this covers all bases I guess.