HDMI output is not a standard feature of the OS itself. Any application written for the Evo has to explicitly enable HDMI output. This is why you can't see your home screen(s) over HDMI, but only video output from the specific media player apps that support it.
That said, HDMI output should definitely be added by the Slingplayer developers to the Android Slingplayer mobile app. Here's hoping!! Is there a forum in which to request new features?