If there was a reason for playing that old clip instead of showing the live performance, the only one I can think of is some kind of technical difficulties. Considering that the sound got all messed up at the beginning of Renai Revolution 21, it doesn't seem too unlikely that something went wrong with the audio.
Regardless, it does suck that they couldn't show the live portion for whatever reason. It makes me wonder if the show is live or pre-recorded.