When I saw a post at Moero Amazon, I imagined it was a BD-only episode, which it was, but somehow it also was broadcast and thus the raw made available by the usual suspects, so I could obtain the video. The "特別" ("tokubetsu") in the title means "Special".

Aira essentially said it all. The episode is a series of vignettes, a pure fanservice. Touma versus Takane was a surprise (spoilers!), and I did not understand why Chihaya did so poorly at karaoke initially. Let us hope that she does not train for wrong thing and ruins her actual singing performance.