Title text:
The draw-by-repetition rule does a good job of keeping players from sliding a tile back and forth repeatedly, but the tiles definitely introduce some weird en passant and castling edge cases.
Transcript:
Transcript will show once it’s been added to explainxkcd.com
Source: https://xkcd.com/3139/
I'd think that having an empty 2x2 right in front of any of your pieces would limit your options for moving pieces. So I would put it in front of White, not in the middle, but on one of the edges. Also, White would not be allowed to shift the tile on their first turn, since that would just put the disadvantage on Black, who would shift a tile, yada yada. Maybe ... maybe you would only be allowed to shift a tile if you didn't shift a tile on your previous turn.
Another thing - would Queens, Bishops, Rooks be able to "jump" the empty space to cross from one side of an empty 2x2? I'm thinking yes.