Hi Lance,
I don’t have an Arduino Yun, but as far as I know it is not based on the ESP8266 chip, which means that the above WiFi library will not work with it. You will probably need to replace the all the network related code with Yun specific code.
From quick googling, it seems like the Yun board is equipped with two different processing units: an Atmel chip (similar to Arduino Uno), and another Atheros chip which runs OpenWRT Linux. The Atheros processor has WiFi support and can run Python and Node.js code, so you will probably need to run the Web Socket related code there. I suggest trying to google for “Web Sockets on Arduino Yun” and try to build up on top of the examples that you find.
Good luck!