Honestly, I'm probably jumping at shadows, but I think that's an allusion to Sakuya Aizawa from Hayate no Gotoku. [/latetotheparty]
I don't think you're wrong, but I think it's more a general allusion to people who like to play boke-and-tsukkomi and expect others to play along. Sakuya Aizawa is maybe the most "meta" about it (fitting, since the series breaks the fourth wall so often) but you see it other places as well, like Tomo's delight when Osaka gives her the appropriate responses in Azumanga Daioh.
You can't get laughs like that, Rinnosuke!Renko, wait for me~Starting from today, I will be observing you.My soba is getting soggy, so can you do it later?Morichika Rinnosuke.Ah… sorry, Renko.A conversation is built on being able to predict what your partner wants to say, you know?