so what's their deal again? cause this reads like the author has no clue either.
I’ll guess: We’ve been explicitly told as readers the 5 sisters are daughters of an overwhelmingly large conglomerate group. Typical manga stuff, really, this corporation ran by (presumably) their parents/grandparents is powerful enough to enable kidnapping and everything else we see in the manga. OK, so what else?
Well, we’ve also seen several flashbacks with the girls and (again, presumably) our main character. So in typical manga fashion they’ve all met before as children but probably only the eldest sister remembers, as the flashbacks IIRC came from her chapters. Our MC is, as usual, clueless to this fact and hasn’t remembered his childhood friends. Maybe they’ve all drastically changed their appearance, or something.
We’ve now learned that the object of the confinement game is to get MC to fuck the key holder. If he does so, we can assume based on the facts above that such an action from MC counts as his personal choice towards one of the girls, likely signalling that he has chosen a wife, and now the game “ends” (or gets taken to the next batshit crazy stage) likely with MC being forced into the conglomerate somehow.
TLDR My personal theory is they (the corporation) has chosen MC as a canditate for marriage (likely due to being childhood friends with at least one of the sisters) and consequently, the next head of the corporation. It is up to MC to choose which sister he wants as the “main wife”. This is the importance of the key and having sex with the key holder, or something. What an insane story.