I (think I) understood the rules clearly enough. The only suggestion I have for your description of the game is to clearly separate between setup (equipment, layout), and play, and to describe them in that order.
My thoughts (and you can check that my interpretation of the game is correct)…
Setup
Number of players: 2
Equipment needed:
1. 22 pieces for each player. The player must be able to distinguish his own pieces from his opponent’s. Also, the pieces must be stackable on top of each other. Checkers, playing cards, etc. are good for this.
2. A 5×5 grid. The grid squares must be large enough to fit stacks of players’ pieces
Play
Goal: To accumulate stacks of 5 or more pieces. The first player to obtain 3 stacks wins.
Rules of play:
1. Players alternate turns (arm wrestle for first turn, or youngest goes first, whatever), and can take one action per turn.
2. During his turn, player can take one of the three following actions:
a. Put a piece down from his hand onto an empty square
b. Move a single (unstacked) piece on the board to an adjacent empty square or on top of another piece/stack (I’m assuming this is legal based on your description)
c. Remove any number of pieces from an existing stack and put them on an empty square or another piece/stack that is at a distance from the original square equal to the number of pieces removed from the stack. NOTE: Pieces can be moved horizontally, vertically, or diagonally across the board, but only across empty squares. They cannot “jump” over occupied squares. Entire stacks can be transferred and placed on other stacks in this manner.
3. When, at the end of a turn, a stack has 5 or more pieces in it, it is removed from the board and awarded to the player whose piece is on the top of the stack.