Fate and the other Gods are playing the Discworld variant of the board game Clue (known as Cluedo outside North America).
The object of this game is to deduce not only which of several suspects has murdered the unfortunate ‘Mr X’, but also what weapon was used, and in which room of the mansion the murder took place. Once you think you’ve figured it out you have to publicly ‘accuse’ the murderer, just as Fate does, and if you’re right you win the game.
Although a Reverend Green is one of the suspects, and the Library is one of the possible rooms, the game does not feature a double-handed axe, last time I looked.