As the Kaji voiceover guy explains in the vid, Satans island, Shina Dark, has arisen when the Exodia Ring was formed (by an eclipse).
This is supposedly a bad thing, as Satan will go on a murderous rampage should his lustful desires not be satisfied. So, everyone sends girls to the island to be brides of Satan.
Satan doesn't really give a shit, so the girls are left to their own devices, unable to return home now that they're supposedly 'tainted'. They eventually get around to setting up Shina Dark as an independent nation, having to deal with the problem of random 'heroes' barging in trying to kill Satan (and with varying opinions on the girls on the island).
It's an ecchi nation building fantasy thing.