I don't have a wealth of knowledge on the subject as I'm not really a javascript dev, but I do know that Javascript and unity work pretty well together using it as a scripting language. Where nodejs would fit into this, I'm not so sure, but hopefully someone else can chime in on their experience
If it's multiplayer, you could use Node along with something like socket.io to handle real time communication between players.
You could maybe, possibly, use WebRTC for peer-to-peer communication if you don't mind excluding anyone running Safari and IE. But with a game written in JS and running in the browser, it seems like it would be too easy for someone to modify the code and cheat without a server side component at least trying to verify that everyone is behaving.