Not nonphysical: just not part of the physical degrees of freedom that can affect things like how die rolls come up or how well a given treatment works on a patient.
The experimenter's intentions (not about the stopping criterion, but about other things) can of course be upstream physical causes, so to speak, of things like what the actual process of the treatment is, and that can, of course affect how well the treatment works. But in the scenario under discussion, all those things are stipulated to be the same in both experiments. And once that is specified, whatever physical variation corresponds to the variation in the experimenters' intentions cannot affect the results.
For a dice that is not a concern (unless animism is taken into consideration), but when humans are on both side of the equation, how do you get rid of all the social and psychological effects that imply, including placebo and the desire to see the study bend in some direction, be it at some unconscious level?
You don't. But again, in the scenario under discussion, these are stipulated to be the same in both cases. (Or more precisely, the underlying unconscious factors involved have the same distribution in both cases.) So again, these kinds of "intentions" don't make the distributions different in the two cases.
Another comment is relevant here. The whole point of things like double blind studies in medicine is to make it the case that, whatever unconscious factors are involved along the lines you describe, they don't change the underlying distribution from which the sampled results are drawn. In the scenario as described in the article, it was assumed that all of these precautions were taken. That is part of the reason for the article's statement that the experimenters' intentions about the stopping criterion can't affect the results.
Of course if you know that in a particular case, those precautions were not taken, that changes how you view the results. But Bayesian analysis can cover this case too: you just expand your hypothesis space and your prior to include things like "the experimenters unconsciously influenced the results in different ways because of their different stopping criterion". The article excludes this possibility in the scenario it describes, but in the real world, yes, we know it is possible to have study designs that don't eliminate this failure mode, and our analysis should allow for that in cases where the study design was such that it might have happened.
