So no, not really. At least not without significant dehydration.
I'm more skeptical of the weight loss claim itself.
And no, chess is not rigorous exercise. If it was, the room would be too hot for them to wear suits and tuxedos. Those burned cals have to go somewhere. For the unconvinced, try jogging or lifting 2000 calories worth in a suit at room temperature or slightly above without taking it off.
Of course, defecation must not be confused with burning body mass.
To state the obvious that I hope doesn't need to be said to this audience: a sample size of one tells us exactly nothing. What's saying this one guy one time didn't have a nasty stomach bug?
A crazy claim like this requires some kind of study not just one guy's story.