This is a single-player only version of Eclipse, a board game that due to the name being a (relatively) common noun, and because it was published before the web was available outside universities, is impossible to find information on now. The best I can find is the patent relating to the game board.
(from the picture above, omitting parts that refer to example images)
The object of the game is to score as many 3-in-a-rows (A) Vertically (B) Diagonally (C) Horizontally as possible, while blocking your opponent from doing the same. All 24 pieces are played before the score is counted.
Note: A piece can be a part of more than one 3-in-a-row. The strategy of the game is to make each piece a part of as many 3-in-a-rows as possible.
To start play, remove all balls from the pins. Each side takes a color. The side with the white balls makes the first play. One ball at a time is placed on any pin of the players's choice; each player placing a ball in turn until all the pins are full. Then count the score. Each 3-in-a-row counts one point ⸺ highest score wins. *
Eclipse is played on a board of eight pins. The pins are arranged so that there are 6 interlocking alignments that provide 38 potential ways to score. A close game will generally run 6 to 5.
* Tie games that are "Mirror" ties are awarded to the first player. (Mirror ties occur when the second player imitates the first player's moves.)