I don't think this is a case of "personal a" even though the result is the same. According to http://www.studyspanish.com/lessons/persa.htm, for the use of "a" to qualify as "personal a" it must be associated with a direct object.
In this sentence, however, there is no direct object. Nadie is the indirect object and eso is the subject. The use of "a" is necessary to clarify that nadie is the one receiving the indirect action, as described in the section on prepositional phrases here: http://www.studyspanish.com/lessons/iopro1.htm. http://www.spanishdict.com/topics/show/17 calls this an "indirect object phrase" instead but the idea is the same.
Talca: Please refer to the post of 'nickfishman'. I think his is the clarifying answer. In addition, you say that 'a nadia' clarifys who like it: no one. Duolingo states that nadia already means NO ONE as well as nobody and anyone. So the no is already implied in the word nadia. Which begs the question, why is 'a' needed to clarify who like it as 'no one' is the meaning of nadia. If A is 'no one' then the sentence reads 'No one no one likes that.
Jim: You need the "le" because it is the indirect object pronoun meaning "to them" (that is, "to nobody"). The literal translation of the sentence is: "That is pleasing to nobody". You must have the "le" to make it a proper sentence. Again, "le" means "to them". The "a nadie" is added to clarify who "them" is. Of course, we translate it in English as "Nobody likes that".
Yes, John, that is correcto. There are a bunch of other verbs that behave in the exact fashion, and they are used constantly by Spanish speakers. Duolingo, however, does not have a "branch" on the tree for them. Study the more common ones: AGRADAR (Me agardan las películas. I enjoy movies.) Literally, movies are enjoyable to me. INTERESAR, DISGUSTAR, IMPORTAR, FALTER, DOLER, MOLESTAR. Nos interesa la clase. The class interests us. Literally, the class is of interest to us. A ellos les digustan los deportes. They hate sports. Literally, sports are disgusting to them. No me importan tus ideas. Your ideas don't interest me. Literally, your ideas are not of interest to me. Me faltan dos dólares para ir al cine. I don't have two dollars to go to the movies. Literally, two dollars is lacking from me to go to the movies. Al hombre le duele la cabeza. The man's head hurts. Literally, the head of the man is painful to him. ¿Le molesta la radio? Does the radio bother you? Literally, Is the radio bothersome to you?
No. These are not reflexive verbs, since one is not doing the action to oneself. They are verbs that always take an indirect object. There's no way to know they need a pronoun (like you do with reflexive from the se at the end), you just have to learn them.
*also, the verb is faltar (not falter).
I thought in Spanish you need "no" and "nadie" together to mean negative, such as one of the examples in this section "no vino nadie", which means "nobody came". Therefore for "nobody likes that" it should be "A nadie no le gusta eso". Can someone explain this for me? Thanks!
You can put the modifier 'a nadie' at the end, but if you do then the verb must be negated: No le gusta eso a nadie.
However (although I'm not a native speaker so I may be wrong on this), to me it sounds better to put 'eso' at the start of the sentence if you're going to put 'a nadie' at the end, more of an emphasis being placed on the subject that is not liked, rather than on the indirect object.