For future reference, if they hadn't gotten all creative with the applet code, you could have simply run this command line:
$ appletviewer http://world87.runescape.com/
What I recommend is to create a dedicated Fluid App for the website. It's super easy, just point Fluid at the base URL, and it creates a dedicated application wrapped around the website. The coolest thing is that you can then simply launch your game directly from Applications.
Fluid is 100% free, and I am not affiliated with them in any way.