I'm probably not the best person to ask regarding this, but I don't quite think it's possible at this time.
The Greenworks plugin you linked is written in C++ which I'm pretty sure isn't compatible with C2. Steam would need to implement an HTML5 wrapper or allow the sending of PHP to their server for certain features.
Now with that said, it might be possible to implement Greenworks if you were to manually build your Node-Webkit app like seen here, but I don't know how you'd have your game communicate with it for things such as achievements.
Again, maybe it is possible and I don't know what I'm talking about. Just assuming based on what I've seen so far.