My working thought on it so far is that it’s heavily tied to whatever “Battler’s sin” is. Then again, maybe Battler’s sin is heavily tied to what “Beato’s motive” is. I’m not referring to the murders either, just her motive for the game in the first place. To be honest, I haven’t come up with any satisfactory ideas or theories so far. So, I’ll need to really focus on hinting in earlier episodes to come up with something workable, which I’m hoping to do before Chiru hits at least.
Regarding the incident on the island and “Beato’s motive” I’m not entirely convinced that they are necessarily bound together just yet. I’m not exactly of the mind that it’s the contrary either; I’m keeping an open mind on this one.
As @mimsy pointed out, there’s likely to be a connection between Beatrice and Maria which ties into Beatrice’s motives. These are the sorts of things I want to keep in mind as I go through the question arc again.
I regret not having something more interesting and less roundabout to say here; this is quite an interesting part of the larger mystery.