With WebRTC it is possible to establish peer-to-peer communication between web-browsers in the same local network: https://developer.mozilla.org/en-US/docs/Web/Guide/API/WebRTC/Peer-to-peer_communications_with_WebRTC
A server is only needed for communication outside of a local network: http://blog.vline.com/post/63765098884/webrtc-if-its-p2p-why-do-i-need-a-server
There is another demonstration in this page: https://hacks.mozilla.org/2013/05/embedding-webrtc-video-chat-right-into-your-website/
However WebRTC is a relatively new system that is not widely supported - so consider it experimental at this stage - but it has the backing of Mozilla, so it might end-up somewhere.
However you are limited to the capabilities that WebRTC provides - and as your code is still JavaScript that runs in the browser you will not have access to any kind of actual networking API (such as Berkeley Sockets) or lower-level control of hardware, such as the ability to create Ad-hoc Wi-Fi networks, new Bluetooth Personal Area Networks, or LE Bluetooth connections... at present.
Google is working on making a Bluetooth API available that runs in the browser. Presently it is only available to Chrome Extensions, but it may soon be available in web-pages in general: https://developers.google.com/web/updates/2015/07/interact-with-ble-devices-on-the-web