Ok, I played a little more.
In each level, you have a SIN counter. You increase Sin by doing Overkills and dealing extra damage. You can also get Sin by using the feather on a person. If you reach the amount of Sin required, you get bonus goodies.
You can only have 4 people out at a time (A B X Y). You can set the people up in formations to deal extra damage and have bonuses - as you can see in that video.
There are towns that you can buy new equipment and items at. You can buy skill books that when used, you can equip them and they activate when you start a fight. Some examples are to direct attacks to one person, make the enemy not that person attack, or randomly gain half the HP from the damage they deal.