Not a problem as Jagex does have a Windows client and I downloaded that and then installed WINE. Once that was there I launched file manager, navigated to my folder where I downloaded the client and clicked on it.
Nice part is that it added the game to my menu bar and launched without a problem. I did have to modify the default settings in the client to what I like to play with, but, that was only 1 minute of work.
So far it seems to be fairly stable and CPU runs in the 20-30% range so that is a good thing there.