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 Online Game
Mahjong Shanghai Dynasty - Thinking games - 1001Games.com
Mahjong Shanghai Dynasty
Shanghai: Second Dynasty : Video Games - Amazon.com
Shanghai Dynasty - Free Play & No Download | FunnyGames
MahJong Shanghai Dynasty APK for Android Download
Shanghai: Dynasty Download | GameFabrique
Shanghai Dynasty - Mahjong game in HTML5 | Lil Games
Mahjong Shanghai Dynasty game - play Mahjong Shanghai Dynasty now - onlygames.io
Shanghai Dynasty Mahjong - play free Mahjong games on MAHJONGG.GAMES!