Well, there is no such thing as a "non word" that is in use - if people (especially many people) use it, it means, per definition, that the word exists! A quick search of "empathetic" gets 622 hits in the 450-million-word Corpus of Contemporary American English, versus 459 hits for "empathic".
We may not personally like a word; there are many words I don't personally like, and wish that they weren't used. And of course there are words that are not appropriate in particular contexts or register, slang terms in an academic paper for instance. Just like it's inappropriate to use nonstandard spelling in most contexts, as you point out. However, "empathetic" and "empathic" are used synonymously in both academic papers and more everyday language contexts (again my source is the corpus mentioned above - it's free for all to use at http://corpus.byu.edu/coca/ ), and there's nothing inherently negative about that.