I have a PhD in this field. I understood everything in the title straight off, apart from the context of which 'parity preserving surface' they were talking about (which was fine). I think this was a concise and well-written abstract, which was easily readable within the target audience. There are very many different concepts that you have to build on and learn to be able to write something like this paper. It's unfortunate that abstracts in the field are not more accessible to a wider range of people, but I don't see an easy solution to that. If you went to the yearly conference on this field and started asking people to define 'MHV' in their abstracts I don't think you'd get many converts. This acronym is cryptic, unintuitive and completely ubiquitous and ingrained in the literature.
