"Surely they have a similar law for films in cinemas, DVD rental etc?"
In fact, the MPAA has vigorously resisted attempts by municipalities to pass laws based on MPAA ratings of movies or DVDs.
There are quite a few reasons for this. First of all, the MPAA is a private corporation. If a law is based on MPAA ratings, then essentially what you've just done is you've written the standards and classifications decided arbitrarily by a corporate entity not accountable to the judicial system into law. Generally speaking, we consider that a bad thing to do. If legislators use MPAA ratings systems to determine what is or is not legal, then the control over determining matters of law has passed from the legislative branch of government directly to a private company.
Second, it raises a thorny issue of what to do about movies that aren't rated. If the law regulates the sale of movies with a certain rating, then does it implicitly require all movies to be rated? If I shoot a film with my camcorder and sell copies of it from my Web site, do I need to submit it to the MPAA?
How will I pay for that? The process isn't free; movie ratings boards have to eat, too. It can cost up to $25,000 to have a movie rated by the MPAA--pocket change for a studio but a significant hurdle for an indie filmmaker.
The MPAA rating system is voluntary, and businesses voluntarily choose to comply with it. When you see things like "children under 17 not admitted without parent", that isn't a law, it's a voluntary guideline.