the name uWink - Nolan always says... that to ask to buy a girl a drink is interpreted as hitting on her, however, asking her to play a game is a nice approach to casual social interaction (the drinks flow soon enough).
And of course woman will feel more like asking men to play a game, then what are they drinking? (to offer to buy them a drink). Nolan pondered in an interview as to how many married later on... after sharing one of his video games as their introduction.