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 Dynasty - free online game
Shanghai: Second Dynasty - IGN
SillyTale MahJong HD | Silly Tale
MahJong Dynasty - Apps on Google Play
Mahjong Dynasty – Apps on Google Play
Jan Sangoku Musou | Koei Wiki | Fandom
Shanghai Dynasty - Free Play & No Download | FunnyGames
Good Game: “Shanghai: Dynasty” | RPGReki's Misadventures
Shanghai Dynasty : Free Download, Borrow, and Streaming : Internet Archive
Dynasty Warriors Mahjong NINTENDO DS Japan Version | eBay
Mahjong Dynasty - Play for free - Online Games
Mahjong Shanghai Dynasty - Thinking Games - 1001Games.com
Mahjong Dynasty:Amazon.com:Appstore for Android
Mahjong Dynasty for Android - Download the APK from Uptodown
Mahjong Dynasty 🕹️ Play Now on GamePix
Mahjong Dynasty for Android - Download the APK from Uptodown
Shanghai: Dynasty (Game) - Giant Bomb
Mahjong Dynasty - 🕹️ Online Game | Gameflare.com
Mahjong Dynasty - NewGames
Shanghai Dynasty 🕹️ Play Shanghai Dynasty on Play123
Mahjong Dynasty:Amazon.com:Appstore for Android
Shanghai Dynasty - Free Play & No Download | FunnyGames
Jan Sangoku Musou - IGN
File:Women Playing Mahjong, Qing Dynasty, Qianlong Period.jpg - Wikimedia Commons
Dynasty Warriors Mahjong Jan Sangoku Musou BEST ''MUSOU'' GAME - YouTube