It is taking its -prediction- of your decision into account in the weaker version, and is good enough at prediction that the prediction is analogous to your decision (for all intents and purposes, taking your decision into account). The state is no longer part of the explanation of the decision, but rather the prediction of that decision, and the state derived therefrom. Introduce a .0001% chance of error and the difference is easier to see; the state is determined by the probability of your decision, given the information the being has available to it.

(Although, reading the article, it appears reverse-causality vis a vis the being being God is an accepted, although not canonical, potential explanation of the being's predictive powers.)

Imagine a Prisoner's Dilemma between two exactly precise clones of you, with one difference: One clone is created one minute after the first clone, and is informed the first clone has already made its decision. Both clones are informed of exactly the nature of the test (that is, the only difference in the test is that one clone makes a decision first). Does this additional information change your decision?