Your first link works for me, and is also added to my connected media. I don't know what else to say. I didn't have to fight with it, just used the 'open url' option.
I just took another look at it. The iHeart streams will play fine on the PC itself, but won't play for me via DLNA while the streamtheworld streams play fine both ways. The way I've been testing these, it's difficult to get audio from the PC itself, so I've been testing the streams going to an external DAC used as a DLNA renderer with a couple of different apps on my iPhone, including JRemote.
In JRiver's playing now section, if I select anything other than the local audio output (HDMI, in this case), and then start playing one of the iHeart stations, it will try to play it then skip to the next station in the list and play that instead. This includes selecting my Denon AVR-4520, Oppo BDP-103, Oppo BDP-105D, and something else that I can't discuss yet.