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 | Free online game | Mahee.com
Mahjong Shanghai Dynasty on Culga Games
Game Shanghai Dynasty at Play 123
Shanghai: Dynasty (Game) - Giant Bomb
Shanghai Dynasty - PC Review and Full Download | Old PC Gaming
Mahjong Shanghai Dynasty | Mahee.com
Shanghai: Second Dynasty (Game) - Giant Bomb
Shanghai Dynasty - Mahjong.com
Mahjong Shanghai - Play Online + 100% For Free Now - Games
Shanghai Dynasty - Top Flash Games: Start Playing Online Today