A suggestion for HyperGG.com :
A button to launch the game depending on what game it is.
Let's use Rust as an example :
http://i.imgur.com/b3gNjKS.pngA button, in one of the corners, or close to the relevant game, that launches the game (Woruld only work for Steam support games) that launches and joins the server automatically. Simple. I think you'd need to find out the AppID then set the launch option to the correct IP address.
This may be what you're looking for if you think this is a good idea:
https://developer.valvesoftware.com/wiki/Steam_browser_protocolThanks!