I really think that Kobayashi, despite being full of dragons and fantasy, is a much better look at relationships than most purported romance shows.
Kobayashi is an extremely realistic person. And the way she slowly grows from "this dragon person is bloody crazy and I want my life back" to "I think I may actually love this family I built" to "I love Tohru and I will stare down a ****ing RPG final boss for her if necessary" is very well done. No need for extreme shows or cheesy confessions or crying drama under cherry blossom petals or any of that rot, because people's actual relationships don't work like that.
I think calling it non-romantic seems a definite stretch, though. Kobayashi is a person who has a lot of trouble putting herself out there emotionally, so she needs to take things slow (which she straight up admits to Tohru at one point), but I don't really think she's non-romantic about it. For one, Kobayashi is too kind and mindful of other people's feelings to lead the couldn't-be-more-obviously-smitten Tohru on for that long without telling her she's not interested, for her own sake, if she wasn't in fact interested.