Wondering - have you seen garment designs with go (the game)? Or any board game, we're not picky. we thought they'd be more popular since they're geometric. i think we've seen more of the shell game, but that seems more like the fans patterns - like lots of little pictures, and not really centered on the game.
Hi! Kaiawase (shell matching game) is part of the traditional court patterns, hinting at classical Heian noble culture with its Tale of Genji miniature paintings. This game has auspicious underlyings hence why it found its way on many kimono and obi!
As a pattern, strategy games are more a secular motif. Go was already already popular among government officers during Nara era, but of what I know it is mostly linked to warrior culture. Same goes for shôgi.
You can find here and there garments patterned with board games, especially men items such as juban or haori linings.
Go patterns are tbh super hard to find on the net - many are mislabeled circles/round motifs (maybe because they look like goishi/go stones?). But go patterns do exist I am certain of that! (sources 1)
Shogi is easier to recognize as its mostly depicted through shôgikoma/tiles though you can also sometimes find shôgiban/boards (sources 1 / 2 / 3 / 4):