A couple of weeks ago we enabled WebGL2 in Nightly. The implementation is still missing some functionality like PBOs, MSRBs and sampler objects, but it seems to work well enough with the WebGL2 content that we've tried.
WebGL2 is based on OpenGL ES 3 and adds occlusion queries, transform feedback, a large amount of texturing functionality and bunch of new capabilities to the shading language including integer operations.
You can test out the implementation here http://toji.github.io/webgl2-particles/. If it says WebGL2 it's working with WebGL2. We look forward to seeing the graphical enhancements enabled by WebGL2 and encourage developers to start trying it out.