Have you read or watched Akagi? It's also a manga/anime about mahjong but focused on the "underground side" (money, betting, yakuza, debts, etc).
I think what is implied is that someone is recruiting mahjong players (willing or not) to play some shady tournament. And Shino's mom is one of those players forced to participate.
Now, for the mystic side of Saki/Shinohayu I think it's more akin superstition. Like in any game involving "luck", there are patterns or beliefs that people think can make they win. Being a fantasy manga gives freedom to the authors to imagine and illustrate the "powers" of the characters. Although Risa (Saki's buchou) is more realistic as she focus on the psychological side of the things (reading opponents and playing mind games).