I'd imagine many classic kids games like "mouse trap" "the game of life" "bonkers" and those style of games could have pieces (rocks?) moving along from space to space on a track, using rope as the track and knots as the spaces.
Knots and ropes could also be used to measure distances for modern miniatures gaming.
Yeah, those would work... But I was looking for a game that would best be played with ropes. Boards are very convenient and it would just be annoying to reverse engineer a game for a completely different medium... I'll keep pondering. Thanks.