Is parsing files an application of machine learning?
I would answer the question at two levels. The first level is "can it be done using machine learning?" I would say that machine learning is essentially about learning. So given that you prepare sufficient examples of sample documents and the output to expect from those documents, you can train a network to learn the structure of documents and extract the relevant information. The more general form of extracting information from documents is a well-researched problem and is more commonly known as Information Retrieval. And it is not limited to just machine learning techniques, you can use Natural Language Processing tools as well. So, in its general form, it is actually being done in practice. Coming to the second level, "should you be doing it using machine learning?". I would agree to what @NeilSlater said. The better and more feasible approach would be to use good programming practices so that you can reuse parts of your parser as your dataset evolves.