Finally found the classic Mahjong game I was looking for. It's called "Shanghai Dynasty". It still runs great both on Windows and WINE so I didn't need to find an old Mac
Mahjong Shanghai Dynasty — play online for free on Yandex Games
Mahjong Dynasty: Kostenlos spielen auf LittleGames
🀄 SHANGHAI DYNASTY MAHJONG ➜ Spielen Mahjong Kostenlos! 🥇
Mahjong Shanghai: Jetzt gratis online spielen
Shanghai Dynasty - PC-WELT
Mahjong Shanghai Dynasty — play online for free on Yandex Games