Reader-response critics (among others) are interested in first readings as opposed to subsequent readings. I note, for what it's worth, that for as many times as I've read Emma, I did not have a strong recollection of this scene. I always conflate it in my mind with the scene at the end of the previous chapter. Both involve a conversation with Mr. Woodhouse, and both illustrate the role Emma plays in keeping the fragile peace around the home.
Is this scene superfluous, then?
Two possible reasons jump out at me for the repetition of scenes involving Emma as a peace maker over strained dinner conversations.
First, the repetition make underline just how monotonous these conversations are, thereby making the reader experience a bit, vicariously, of the tediousness of Emma's existence. As we have said before, it is one thing to be told that Emma's father is a bit of a hypochondriac and a high-maintenance relationship, it is another thing to feel the constant presence of such a person in scene after scene.
A second reason for this scene may be a foreshadowing of Box Hill that underscores some of the gender politics that Emma has to live with. In both scenes a benign but irritating person (Mrs. Bates/Mr. Woodhouse) is curtly cut short by a momentarily exasperated listener (Emma/John Knightley). The difference? While Mr. Knightley rips into Emma for her momentarily lapse of patience, Emma "could not wonder at her brother-in-law's breaking out" (69).
Obviously, there is more than one difference between these two scenes, but the central one that jumps out at me is the gender of the person making the curt remark. The woman is apparentely expected to hold her tongue endlessly, while the man, it is understood, can only be expected to take so much before his outburst is considered unremarkable.
Both characters are nearly instantaneously sorry for their remarks. John Knightley pauses and grows "cooler in a moment" (69). Emma "blushes" and "was sorry." John Knightley, after the pause, though, presses on: "[...] growing cooler in a moment, added, with only sarcastic dryness [...]" (69).
So, stop the presses, there is a double standard applied to gender! The same actions considered a huge faux-pas for a woman is considered an understandable irritation for a man. When the man pauses and repeats his cutting remark, the onlooker sees her responsibility as stepping into the breach to separate and soothe the conflicting parties: "[...] the soothing attentions of his daughters gradually removed the present evil" (70). By contrast, when the woman lapses, the onlooker (George Knightley) sees his responsibility to correct the offending party with a stern rebuke: "It was badly done indeed" (246).
Nobody is saying "badly done" to Mr. Woodhouse for scolding his married daughter for following her doctor's advice or to John Knightley for cutting off his father-in-law and host.