The game is know as "breakthrough".

The 8x8 board is initially set up with the two front rows filled by white piece and the two back rows filled with red pieces.

White player go first; then play alternates, with each player moving one piece per turn.
A piece may move one space straight or diagonally forward if the target square is empty.

A piece may move into a square containing an opponent's piece if and only if that square is one step diagonally forward. The opponent's piece is removed and the player's piece replaces it.
Note that capturing is not compulsory, nor is it "chained" as in checkers.

The first player to reach the opponent's home row — the one farthest from the player — is the winner.
If all the pieces of a player are captured, that player loses. A draw is impossible because pieces can only move ahead (or be captured), and the piece closest to the opponent's home row always has at least one forward diagonal move available.