I know “酒” usually means wine in Chinese, but what does "酒" mean in "扮家家酒"？ I could not see how the word for wine is referring to in this children's game.
喝喜酒 = 赴喜宴
設/擺酒席 = 設宴
The 扮家家酒 game is to pretend to have a lively family gathering.
酒 should refer to a 酒席 (banquet) -->喜宴 -->聚會
扮家家酒 Also called 过家家
小朋友一起各自扮演不同的角色，往往是模仿家里成员，做一些小孩子们眼中大人应做的事情。 Children play different roles together, often imitating family members and doing things that children think adults should do.
Banquet, party, socializing, and drink are adult things.