Race to the corner with a rook

A rook moves only south or west, heading for a1, and whoever lands on a1 wins. Unlike Wythoff's queen this rook has no diagonal move, and that changes the winning idea to mirroring. Keep the rook on the main diagonal a1-h8 after your move: from a square with equal file and rank, whatever the opponent does on one axis you undo on the other, staying on the diagonal.

The diagonal squares are the safe positions. Symmetry is the strategy: match the opponent's move on the opposite axis and the distance to a1 shrinks in step, always leaving them to move from a diagonal square, until you step onto a1 yourself.