It's somewhat similar to a Flash-only website, since it has less support and most notably lacks many of the features HTML makes easy (search engine indexing, browser search-and-find, ease of development, layout, and separation of content from style).
It works well on OSX 10.10 with an HD4000 in Firefox, Chrome and even in Safari. The "framebuffer not complete" warning looks like you're using an extension which isn't supported everywhere, probably OES_texture_float or WEBGL_depth_texture?
Author here! It's very true that the GPU does the heavy lifting, although I'm not sure exactly where an "in the browser" line could be drawn (conceptually any page uses the browser as an execution engine and library).
It's a bit trickier due to restrictions in WebGL (OpenGL ES based) compared to the desktop (e.g. no bitwise operators makes it a pain to get randomness that doesn't bias the result), but it's basically the same.
Please let me know if you have any questions, (see my email at http://jonathan-olson.com/about), and please feel free to use my code however you like (things I wrote are MIT, but I use CC-by and CC-by-non-commercial HDR images).
If you're interested in ray/path tracing or photorealistic rendering at all I would seriously recommend Physically Based Rendering. It's probably one of the most satisfying book purchases I've made. The authors go through every aspect of implementing a quality path tracer: image sampling, surface shading models, statistics and integration methods, intersection testing and acceleration and more. It's an absolute treasure trove of information. (Be prepared to do a lot of math.)
Very nice! I'm also working on a similar scene graph (Canvas/SVG, WebGL soon), which also has bounds, DAG-support, and implicitly inserts the needed layers for performance (http://phetsims.github.io/scenery/).
I look forward to seeing what other performance optimizations I may be missing!