Arqade is a popular site, and is not only accessible to children (in this context, any user under 13), but has a major focus on a topic children are generally interested in.
Any website that is either hosted in, or within jurisdiction of the United States of America must abide by the 1998 Children's Online Privacy Protection Act, where compliance is mandatory if the website is deemed directed at children under specific qualifiers, and violation can be quite expensive.
To quote part of the definition of Who must comply;
If you operate a commercial Web site or an online service directed to children under 13 that collects personal information from children or if you operate a general audience Web site and have actual knowledge that you are collecting personal information from children, you must comply with the Children's Online Privacy Protection Act.
To determine whether a Web site is directed to children, the FTC considers several factors, including the subject matter; visual or audio content; the age of models on the site; language; whether advertising on the Web site is directed to children; information regarding the age of the actual or intended audience; and whether a site uses animated characters or other child-oriented features.
Let's all be honest here. Kids love video games. But so do people of all ages, and here at the Arqade, there is a certain expectation of maturity. Kids can still have their problems solved. I often see questions posted by the parent, who in turn is able to for a better immediate understanding of our rules, and post without need of a serious edit to cater for poor spelling or grammar.
By having a set requirement that users be at least 13, Stack Exchange forces an intended audience, and despite focusing on video games, and having cartoon-ish graphics and backgrounds, would not count as having to comply with the act. In turn, special precautions do not have to be made, to ensure compliance. There is also no risk of accidental noncompliance, which could result in a hefty fine for the owners.