i see nothing wrong with it. 12 year olds are capable of being left at home alone, who cares if parents leave them at LAN places - as long as they are picked up before closing time.
at around 12-14 I was going out at night and hanging around cardstores (yes poor me) all night. It wasn't a babysitting thing, it was just because i felt like it. I'm sure 12 y/o's can take care of themselves at a net cafe. jeez