I wanna know if this is really a Yuri Manga or not...
The definition of Yuri that I use is stories that focus on the emotional, social, sexual, and or all three aspects of lesbian relationships. And this is in line with how the genre is used in Japan (so this excludes Shojo-Ai which is lesbian lolicon in Japan).
Yuri isn't all romance requiring pairings to come through at the end; it's not all sweet fluff and hand holding isolated in secret gardens protected from a hostile world where love reigns supreme. There can be a lot of struggles and things don't, like anyone's feelings of love for another, work out.
This story has a young women in love with and adult married woman and the story focuses on the young woman's feels and desires for the older woman. In addition to the difficulties there there are familial dynamics, other relationships struggles, and difficulties in expression and falling out of love. A layered story with other presented views doesn't make this series any less Yuri as ultimately the story comes back to the feelings of attraction, that don't have to end in romance, for and growing between two women.
That doesn't make every story with a lesbian pairing Yuri, but here the focus stands.