mjhjmtu

In about 1966 or so, a stand-in teacher at our primary school spent the afternoon reading short stories to us. There was a wide genre, but I was particularly fond a one which was science fiction/mystery.

It involved a group of people who were talking about mysteries, and another man from outside the group bet the he could tell a story, and one of them would disappear and the others would not notice. The final line was something like "he kicked over the stool and walked from the room".

This sounds like Exit by Harry Farjeon (adapted into a film in 2012)

It involves a group of people attending a dinner party including a newly-wed couple by the names of Jake and Jessamy. Mr Geeles claims he can erase people from existence, referred to as "de-creation" in the story. Of course no one believes he can do this, as the de-created are also wiped from all memory of ever having existed. He ends up trying to demonstrate his claim. At the end an empty footstool is kicked over where Jessamy had been sat.

Maybe a stretch, but could it be Child of an Ancient City by Tad Williams?
This short book is about a group of men who are being stalked by a vampire in the woods as they travel. Eventually, the vampire gives them an ultimatum: If he can tell a story sadder than any story they tell, he gets to take one member of their party, then he will leave them alone.
The book is essentially a conglomeration of short stories, as the men attempt to tell the saddest story, but in the end the vampire wins by telling a true story of his own life, and how he became a vampire. However, when one of the men volunteers to be the one taken, the vampire leaves without a trace.