The letters represent events or states of affairs (or, as one could say, variables, in which we may have varying degrees of belief), not people. I illustrate this in Game 1 for X and A, just so you get the hang of it.
Defendant pulls trigger (X = this action by defendant)), gun fires (A = what the gun was caused to do), cartridge casing ejects (B), bullet hits victim (Y).
Here there is nothing to block the causal chain from X to Y. B is irrelevant to whether the firing of the gun caused the bullet to hit the victim.
If the arrow B to A were to be reversed, because the defendant's alibi made it more likely that the other person who hated the victim was the murderer, there would be a causal chain A, B, Y, which the defendant would hope would reduce further the alleged link X to Y. The prosecutor's attack on the defendant's alibi was an attempt to block the suggestion that the other person was the murderer.
The proposed causal chain generated by the propensity evidence is blocked by C to B. This reflects the legal position that propensity alone is insufficient to prove current offending. There must be some evidence of current offending before the propensity evidence has anything to corroborate. If there is some such evidence, the admissibility of the propensity evidence will depend on the extent to which the prosecutor can reverse the causal link from C to B, for example by showing that previous commission of fraud (B) strengthened the defendant’s propensity for dishonesty. If the link then went from B to C, there would be no blockage in the causal chain X, A, B, C, Y.
So, how secure is the position of judges and juries in coming to verdicts? Computers can't perform experiments, they can't use what the authors call "do-operators" to change things in the experimental environment. Where there are causal chains, data may be available to be used to generate conditional probabilities which AI can handle. But where a blocked chain cannot be ignored as being irrelevant, an experiment will be necessary to provide more data. A computer could not, therefore, play Game 2 because of the blocking effect of D (which would require an investigation of the likelihood that the defendant did consume the substance), or Game 3 because of B to A (unless it was able to compare the video image with the defendant, although there may be legal objections to that, or with the other person), or Game 4 because of C to B. Judges and juries surmount these difficulties with something ineffable called judgement.