I am uncertain, what they are going for. One time this looks mostly like a comedy (I even thought of Nisekoi, considering the premise), but then it becomes much darker, and then it becomes practically a comedy again. Maybe this is intentional for the sake of showing the difference between the characters, and how they will start blending in as relationship develops. I am not sure if that's the case, though.
The girl, who reminds me of the character from The Twelve Kingdoms, makes little sense to me. She does not feel like a granddaughter of Yakuza, who lived her whole life with Yakuza. I guess she could have been sheltered, and it was mentioned, that her family owned whole Kansai region, but it still does not sit right with me. I also do not understand why she sold her kidney: it was not only stupid and reckless, but made little sense, since if she needed money, she could have asked her granddad for them. While he insisted on her staying in Tokyo, it did not look like he was cutting her off.
It definitely has potential, so I will still give it a chance, at least for 3rd episode.