I basically took the entire thing as an allegory for purgatory. It works, in the sense of this cyclical musing over their life choices. Each personalized scenario is essentially the "best case scenario" for their diabolical plots, essentially getting away with their murder without any punishment. Thus, revisiting The Cave was revisiting their decisions repeatedly. The goal would be for them to see their errors, hence the choice at the end, to refuse their desires, achieving the ability to "ascend"... This could either be to existence again, or maybe just a sort of peace in the afterlife (I think the game is intentionally vague here). The entire game itself is the allegory for this sort of cyclical purgatory, one the player too must walk around "the wheel".
The characters, on the other hand, almost certainly represent the Seven Deadly Sins: Here's how.
Knight = sloth
his inaction destroyed an entire nation
Adventurer = greed
she cannot share her glory
Time Traveler = envy
She cannot stand someone else’s achievement
Scientist = gluttony
She will gladly indulge while the rest of the world suffers
hillbilly = lust
Pretty obvious, but his lusts drove him to insane jealousy for a woman who didn’t even know him.
Twins = wrath
They kill with no remorse, or reason, simply because they found something frustrating
Monk = pride
Cannot stand to not be recognized as the greatest, even when he hasn’t even begun to earn that mantle
Each of the characters represents a deadly sin, thus the same issues that we (the player) are supposed to face. The purgatory for us is more or less our conscious: the choice at the end is our own choice over our actions, and the cave itself is the journey we take through life being tempted with all of these things, playing through literally a fantasy of the darkest parts of our souls.
This could all be crap, but I think for the most part at least the seven deadly sins part makes sense, and the purgatory analogy makes the tedium of the game seem much more sensible.