I understand this to be Yut-nori, a game supposedly based on horse racing and traditionally played at New Year’s celebrations. Possibly dates to the Three Kingdoms period, and possibly related to Pachisi.
Yut features binary throwing sticks, which can be pocket size to over 15cm. The full size sticks make a delightful rattle in the hand, and can be downright noisy landing on a wooden table.
The “board” is usually handmade on cloth, and called malpan /말판. Pieces are called mal /말 and are not strictly any particular item. Fabricated mal often look like Go stones. Inexpensive examples are similar to something found in a Christmas cracker.
Mine is made with felt and quilting cotton, and has no machine stitching.
http://www.medieval-baltic.us/koryut.html
How to play traditional Korean game Yut Nori (윷놀이)
The game of Yut.
this link has a video- notice players throw onto a cloth (jacket)
https://blogs.transparent.com/korean/yut-nori-윷노리/