Also lets not forget being able to sense thoughts from people around you at all times, so hey you just take a walk around town and listen in to people's heads and whadayakno, that guy's the murderer because he thought about it in detail that could be known to no one but the killer himself, now all that's left is to prove how with access to all the knowledge of what happened provided by the ghost, the crime scene and potentially the murder weapon as well. And no I can't really come up with ways to replace this umbrella of metagaming abilities with chess. I can, however, suggest replacing the swords with some kind of decorated mace scepter, because clearly you're the king in chess terms.