There are just a few changes in the rules for 2 players:

First, the Catcher has to catch the Runner twice before the round ends. When the Catcher touches the Runner for the first time, he takes away his ID card as usual. Then the Runner is moved to the Classroom (box nr.1) where he takes his turn from the Red circle, like in the beginning of the game.

Important note - the Catcher's turn completely ends and he cannot use Ice Skates to take a second turn.

Second, the game ends when each player has been the Catcher twice! The players alternate between rounds for who plays the Catcher and who plays the Runner.