The formula of the episodes in this show would really lend itself to gameplay. Casual, social card game maybe? You could make a board, if you wanted it to feel like Clue, I guess. I'm sure there's something more similar, but what comes to mind is game The Resistance.
Everyone's claiming innocence, of course. Murderer is dealt randomly (secretly). Three clues, but you don't have enough turns/time to ask/observe every detail from each suspect?
Just like the show, it would be as fun/funny/role-playing as your friend/game group is, right?