- They knocked over the queen, not the king
- The black king is in check, so it must be black's turn or the game is already over due to off-screen pieces
- In the final panels you can see the lady who said the move was invalid was playing white
Thr guy was playing black and moved white's pieces because he already lost, justifying his move as an "overthrow of tyranny".
It's not always discussed as such, but Hilbert's Hotel is a mathematically well defined topic and can be proved rigorously. An infinite set of rooms can be the set x1, x2,...xinf, and people can be y1, y2...yinf. You can pair every entry in these two sets. x1&y1, x2&y2,...xinf&yinf. You can't number a room without having a person in the room, and you can't find a person who doesn't have a room.