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
SHANGHAI DYNASTY +1Clk Windows 11 10 8 7 Vista XP Install – Allvideo Classic Games
Mahjong Shanghai - Play Online + 100% For Free Now - Games
Mahjong Shanghai Dynasty | Play with Libero Fun!
Mahjong Shanghai Dynasty | Play with Libero Fun!
Mahjong Shanghai Dynasty: Play Online For Free On Playhop
Shanghai Dynasty - Free Play & No Download | FunnyGames
Shanghai Dynasty - Mahjong game in HTML5 | Lil Games
Good Game: “Shanghai: Dynasty” | RPGReki's Misadventures