This episode basically comes down to two issues: a pre-opener piece about TV sets and movies and a main story about rings. Both were likely put in the same episode to create a contrast on value and priorities, both for humorous and serious reasons.
Concerning the TV set, Nasa has apparently not had one while living on his own and has little use for one. Although this is a slightly increasing trend in Japan (the percentage of homes with TV sets has decreased about 3.5% over the past decade), it is still highly unusual, even for someone as study-oriented as Nasa. Whatever Tsukasa's real origin may be, she clearly got immersed in TV and movies while living with Chitose, including some pretty trashy stuff (which Chitose and one of her maids are also apparently into). Whether her insistence is more for personal interest or a way to share with Nasa is debatable; I am guessing at least 2/3 the first and 1/3 the second, although the latter could just be an excuse designed to appeal to Nasa. It is, however, the first material item beyond basic necessities that Tsukasa has gotten insistent about.
Contrarily, she is not at all interest in a ring, which she does not see as having entertainment or practical value. Kaname is the one that talks Nasa into recognizing it as important, but I was pleased to see Nasa coming to the conclusion that it was necessary based on his own reasoning: it is a reminder of the spouse which can be called upon at a glance when the two are apart. What Nasa continues to fail to understand is that Tsukasa values gestures and the meaning behind them far more than anything material. That is why she is not bothered by living in Tsukasa's small apartment, sleeping on a futon, or happily settling for the cheapest wedding ring available after miserably failing to scare Nasa off of pricier rings with sticker shock. (In that she is underestimating how much he now prioritizes her.) That mindset also has some interesting potential implications; could it be connected to why Tsukasa is no longer living with Chitose? Could be it connected to her not having a sense of permanence in this world? There's still too little information available about her background to judge at this point.
In the midst of this, Nasa and Tsukasa get to kiss again and perform all manner of blushing to keep the romantic spirit running. All of this also allows the dumping of another extensive set of pop culture and place references:Tsukasa makes obvious references to Star Wars, the Indiana Jones movie series, the Dutch horror movie trilogy The Human Centipede, and The Terminator. She also clearly refers to director James Cameron, whose feature movie directorial debut came with 1982's Piranha II: The Spawning; pictorial reference is made both to that and to his later global box office-topper Avatar. (This is an interesting choice since Titanic performed substantially better in Japanese box office than Avatar.) Space Jawsnado: Maximum Mission is a clear riff on Syfy's hit film series Sharknado. Nasa's mention of Mito Tsukino is a reference to the leading VTuber from the Nijisanji group, who is portrayed as a high school Student Council President. She did mention having seen The Human Centipede in one of her streams. High-end jeweler Honey Winston is almost certainly a reference to Harry Winston, a high-end jewelry chain which does have a store in Tokyo. The market that Tsukasa and Nasa go to at Okachimachi is probably Ameya-Yokocho, an open-air market which extends under the nearby railroad tracks. The episode also features Momoi Harappa Park, which is a real place.