Here is an overview of the game’s story, via its Steam page:
A closed island where baby boys are not born…
A unique culture that is completely different from the mainland has been flourishing on the island. In the middle of the island, there is a district where men are gathered.
Some women just want children.
Others are looking for love.
Knowingly deceived by a lie, and deceived in return, all in a single night’s dream.
At the end, to whom is it that you will be talking of love?
A western release is also planned, but has yet to be dated. Given that one of D3 Publisher‘s other Switch titles, Tennis, is also releasing on January 25 in both Japan and western territories, and that the Japanese version of The Men of Yoshiwara: Kikuya has English subtitles, it is possible the west will see its release as soon as tomorrow.
Watch the opening movie below.