To judge whether in check at the start of your turn, the enemy Joker should be imagined to still have the move of the previous turn.
To judge whether you are in check during or at the end of a turn, you should imagine the Joker to move as the piece that is moving in that turn.
Now Greg's example was special, because the Joker itself moved. If the white King had been on c2, the Joker on a5, and a white Knight on a4, and on the move before Queens were traded at c3, where the Knight recaptured (Na4xc3)... Is this checkmate or stalemate?
We can summarize this as:
Now Greg's example was special, because the Joker itself moved. If the white King had been on c2, the Joker on a5, and a white Knight on a4, and on the move before Queens were traded at c3, where the Knight recaptured (Na4xc3)... Is this checkmate or stalemate?
The Diagram considers it stalemate, because it lets the white Joker move as Knight after 1... Qxc3 2. Nxc3.