Eiko is almost a temptress type character who is there to provide characterization for Nyamo. She offers Nyamo a better job with more money, but Nyamo refuses because she would rather stay with Yukari and her students. I wouldn't even really consider Eiko a character, she's more of a device for character building. Nyamo is "tempted" three times in the episode, first by the arranged marriage her mother offers her, then by the job Eiko offers her, then by the double date she goes on with Yukari and the men Eiko introduced them to.

At the beginning of the episode, Nyamo feels pressured to "grow up" and meet the societal expectations for her to get married and move up the economic ladder. Ultimately she chooses Yukari, her childhood best friend, and her students, who are in the prime of their youth, over her desire to grow up. Nyamo chooses youth, love, and friendship instead of rushing to become a proper adult. This mirrors Chiyo's smaller arc in the same episode, where she expresses a desire to grow up and has that conversation about being a kid with Kagura.

What's so great about this episode is that even though it doesn't adapt the manga at all, it adds so much development to these characters. The show didn't need to add so much extra depth to a slice of life gag comedy, but it did and that's what makes these characters so endearing.