I'm also using the same websocket implementation for another pure GWT project. This has been absolutely solid for me.
I also have server side, websocket clients running as well, if it helps, I am extending WebSocketClient in that case.
The HTML implementation will use hooks to the browser to create client side connections.
Of course, this has nothing to do with PlayN, so I can't comment if this is related to your observed issue. I bet you will have to implement for Java/HTML platforms separately. Start out by using the WebSocketClient class and testing in Java, if it works, then you have your next move.
Scott