Answering my own question based on two articles I have found online. First is this article by Andrea Park on CBS News’ website. According to Bourree Lam—senior editor and mahjong enthusiast Refinery29—the scene has multiple layers of symbolism; bold emphasis is mine:
“Rachel draws a tile in mahjong. It's a set-building game; it’s very much like poker, so you can draw a card that gives you the win. So Rachel draws the win, but instead of winning, she lets Eleanor have [the winning tile], and so that mirrors the dialogue because what she tells Eleanor in that moment is, ‘Your son has proposed to me, but because I don’t want him to lose his relationship with his mother, I am going to say no and in the future, when he marries someone you think is appropriate, you're going to remember that that's because of me.’”
And goes on to further explain:
The scene is full of allegory, with Eleanor taking the dealer’s seat—the east seat of the table—representing the traditional values of Singapore, while Rachel sits in the west seat, representing America. Eleanor tells Rachel she’s not an appropriate match for her son because she is American, not “our kind of people.” While she is saying this, Eleanor collects matching tiles of the same kind, again signifying that she wants to extend her family with more of her “kind of people.”
And as further explained in this article by Emma Dibdin on New York Magazine’s Vulture website; again bold emphasis is mine:
Rachel is not bluffing; she’s truly prepared to walk away from this relationship, though the pain it causes her is clear. And when Nick eventually marries someone Eleanor deems worthy, she says with quiet intensity, “it will be because of me. A poor, raised-by-a-single-mother, low class, immigrant nobody.” With that devastating kicker, she walks away from the table, revealing that she had a winning hand all along and chose not to play it. Unbeknownst to Rachel until later, this sacrifice is enough to change Eleanor’s mind about her—but in the moment, it doesn’t matter. “When Rachel walks away from the table, she is now fully who she’s supposed to be, and she doesn’t need Eleanor’s approval, she doesn’t need that ring. She doesn’t need anything,” Chu says. “She’s walking away with an understanding of how unique her dual culture is.”
Additionally, the tile in question—the one that seems to have a W and M on it and as mentioned in the Vulture article—is the Bamboo 8 tile. To my knowledge the number 8 is considered a lucky number in Chinese culture, so that could be something. But I found this Travel China Guide page on the number 8 that explains the number’s meaning as follows; bold emphasis is mine:
People with the lucky number 8 have strong intuition and insight, so they have the potential to explore things undiscovered. In general, they are bestowed with a special gift of being inborn businessmen, and can achieve all their plans step by step. They are usually mild and honest to others. Their characteristics would never lead to arguing with other people or causing them to be depressed. Nevertheless, in order to avoid hurting people around them, they always hide their real emotions, whether they are sad or happy.
While this is coming from a travel agency site (If anyone has a better reference, please provide it in the comments…), it doesn’t seem like a click-bait site and the definition sounds an awful lot like the way that Rachel’s character is behaving during the game.