first case....... chessplaying ghosts
Yes. Correspondence with the dead proven by Prof. Eisenbeiss.
Who from the non-god position will correlate the simplest explanation with the observations? Two guys played a chess game? That is all the article outlines. One of the guys claims it was not him playing chess, but a dead person. There is nothing beyond that to examine. Not only is that not proof it is not evidence either. It is a claim.
You have a point there. Even if there were a real other party (the dead person) playing, maybe it was an alien or demon using mind control.

Perhaps, but there is no evidence for that. The point is this:
Those explanations are needlessly complicated. The simplest explanation is that the personality of the deceased person has persisted and is able to communicate the information that was receievd.