I might be able to do most of that show with all of those machines and maybe a stand-alone recorder. Fill in the missing parts as needed in post production.the main host, Scott Johnson, uses a Mac. But I also know he has a PC and a mixer.
One of the computers just does Skype. It's connected to the mixer so that the Pre-Fade-Mix goes back to Skype with Skype's own voice missing. That solves the return echo problem and the caller will hear everything but their own voice. The second computer plays the stingers, bumpers, themes, interstitials and other music into the mixer. I think any DJ sound package will do that. Maybe just iTunes or Windows Media, suitably cued up like a playlist.
The Stand-Alone Recorder just sucks it all in and makes the sound file. I guess the second computer might also be the recorder, but that would be pushing it. You would have to be really careful not to press any common hot keys by accident. "STOP" in the music player [Spacebar] can't also be "STOP" [Spacebar] in the recording software. So no, you would need a stand-alone recorder.
That's 2-1/2 computers, a good comprehensive mixer, some way to distribute the headphones if you have more than one host, and obviously a Skype account, etc. I don't think you can do that show live with less equipment than that.
Koz