(yWorks employee here, having worked on that Graph Drawing Contest)Thank you for the kind words.
I've tried to make it mobile-friendlier, after our marketing team told me that most people who come via Twitter use a phone. But we kinda ran out of time, so I only managed to fix the most egregious problems. By now I also have a few ideas how to get the edge paths to be much better (and built-in Bézier spline routing would have helped, but that was only released publicly ... two days ago). Admittedly, while that layout has been produced by yFiles' hierarchical layout it needed a bit massaging to do so properly (about 200 lines of custom layout code, if I remember correctly). However, a proper library that gives you that flexibility helps tremendously, of course. Sometimes, trying to get Graphviz to do the right thing can be pretty complicated and may involve hacks like invisible edges to force a certain layering (although that was way back and I didn't know about "rank=foo" back then; perhaps the invisible edges were really not needed).
In any case, yEd Live (https://www.yworks.com/yed-live/), built on yFiles for HTML, also has an undocumented, incomplete, and rudimentary Graphviz import. I've got a fairly exhaustive list of issues and missing features, but little time to tackle it, sadly. This is further complicated by the fact that the DOT language uses attributes to describe the graph structure, visual attributes of items, and to control layout settings. That makes mapping Graphviz to anything else a bit hard.