Does anyone know which game this is.

This is not a game in itself, these are used to count points in mahjong. Perhaps your parents also had a mahjong set?

What a beautiful set! If you like board games at all, perhaps you can find someone to teach you mahjong and put that set to use. It's fun, a lot like Rummicub (if you know that game)

The other photo you post is of mahjong tiles on sticks. I've never seen tiles on sticks being used to actually play mahjong, so I would guess those are some sort of novelty item. What's on the other end of the stick?

The line on the box is a quote from Su Dongpo: 次韵送徐大正（cì yùn sòng xú dà zhèng）原文、平仄韵律对照、注音、翻译、总结、赏析 - 苏轼（sū shì） - 诗词志

Think it means something like "a thousand new poems and a fishing rod;" it's from a verse he wrote for a friend and that's a couple of pleasures he wants them to share I think. No  doubt a quick hand of mah-jongg too if they had such a thing.