Going on the website just redirects it to open the client (application). Tried this on Chrome and Safari.
Edit: ' El Capitan users - you must have java 8 to play as java 6 no longer is able to be installed. So check this first if the client wont load just to be sure!
Cannot play in browser
It's not possible to play in the browser anymore, it'll just redirect you to the game client due to java being removed from the browsers. Download new client' from http://services.runescape.com/m=forum/forums.ws?25,26,4,65321326