Hi guys look you might not get responses, because there are tons of posts on this. Did you search the forum?
I checked the O.P.s link and I can't get it to play straight form chrome .. so IMO, thats a problem with the site. (or I need Quicktime on my machine which I purposely do not want on my rig)
Short answer ... if it has a specific API (like a built in player, its probably not going to work unless you have the API key (and you know what you are doing). Most real radio stations and things like NPR are going to fall in this category.
Or like Lewin's link, it falls on a flash player ... some times you can get this to work, but often it will not ... you can try changing the browser engine in JRiver options from Chromium to IE or vice versa, and make sure your pluggins/extensions are up to date. The fact that they make these "players" useable on Quicktime or Flash-based players, doesn't mean its going to work internally in JRiver ... there is no internet standard for streaming, and lots of sites go to great length to prevent "for-profit" software like JRiver circumventing their APIs
There are work arounds, like running external programs with JRiver, but the best and easiest way is just to run it using the WDM driver, and not messing with the connected media area. Some like Spotify, Grooveshark will work, but might as well just play it from the browser and take advantage of the JRiver playback engine.