Update: Version 0.975 resolves this issue. 

Unity 5.6 introduces a new bug by changing the communication between an Unity App and the surrounding website. This will cause problems while loading the java script code of the plugin.

For now the problem can be avoided by using templates which include the java script code before the unity app is started. Simply import the unitypackage files and select the WebGL templates via the WebGL Player settings. You can find the needed files here: WebRTC Network ,  WebRTC Video Chat template.

You can find more information about Unity WebGL templates here (not yet fully up-to-date).

Version 0.974 of WebRTC Video Chat and WebRTC Network is now available in the Unity Asset Store.

Major changes:

• Full Stun / Turn support for all platforms
• Android version is now an optimized build
• native VideoChat applications support now echo-cancellation (see ChatApp.cs)
• Improved logging

Additionally, there have been a lot of small bugfixes and improvements in the documentation / sample applications.

I also have a few new sample applications to test new features. Please send an e-mail if you want to help testing!

Current test applications:

• Video conferences – changes the ICall interface to automatically create n to n connections between all users that use StartServer with the same address
• One to Many streaming – using a more low level interface allowing 1 to n connections or the creation of your own custom Video Conference tool. (The ICall interface builds on top of this)
• Custom Video Streams – allows streaming of raw images
• Raw Audio – allows receiving of raw PCM Audio from WebRTC (instead of automatically replaying it)