It's so bizarre that a piece by Itou Hachi of all people would spark this level of dark speculation. It's pretty obvious that the setting, aside from the same-sex marriage and the animal ears, is a semi-utopian version of historical Japan, with all the trappings. The clothes, the archaic lifestyles, and the arranged marriages. But from what I gather in other "legally married" pieces she's done (which are in the same world, from what I gather), the partners are arranged but not forced, in that they have the right to refusal. So it's likely a matter of friendship between two families, rather than necessarily a business arrangement or setting up for an heir.
I think this society would work well with Japan's long history of adult adoption. Instead of a biological heir, which you're rolling the dice on whether they have an aptitude for carrying on the family business, you simply take an apprentice who shows promise into your family officially, and thus they become the hear to the business. In cases of same-sex partners who obviously wouldn't produce one themselves, it seems a good solution.