I can’t tell what is going on from the logs. My best guess would be a stripping issue - does it work if you disable “Strip Engine code” in WebGL player settings?
You can file a bug with a repro case, and post the case number here, then we can take a look.
It does indeed work when I disable the engine code stripping. Thanks!
I also reported a bug, the case number: 733661.
Got a mail that they checked this. It will be fixed in Unity 5.3. They also provided a simple temporary workaround: just add an empty OnGUI method in your code.