It is fairly violent, yes, but more mature teenagers will be able to grasp the underlying themes of it. I feel as if most people on this site focus too much on whether it's a appropriate and not enough on what the actual content is. The entire premise is posing questions. When it comes down to it, can you trust anyone? Do you know who your real friends are? Stop being overly concerned about whether something is "appropriate" and start actually thinking about the film.
It's mostly a "what if" scenario. And might I also add that the reviewer got parts of the plot wrong? There were 42 students, and their bus wasn't "hijacked". That would imply that an outside force was involved. The government was the one employing the program.
Though the movie focuses on main character Shuya Nanahara (Male Student No. 15) and Noriko Nakagawa (Female Student No. 15), it gives sight from a variety of points of view throughout the variety of the class. As well as posing questions about who can be trusted when it came down to the nitty gritty, the film also voiced a message about the dangers of totalitarianism, and the nature of a corrupt system. If one were to read the novel that the movie was based on, there would also be a taste of seeing the United States from a different light (as The Republic of Greater East Asia is a great rival to the "American Imperialists).
Overall, I don't think that age should really be a judge for this particular movie as much as maturity should. Do you believe your child is competent to wrap their head around the deeper meanings of the film? Then let them watch it (and DEFINITELY let them read the novel; it is so much better). Although, if you're talking a minimum age, I would say that it should be treated as a PG-13 movie.
But really, read the novel. It's a million times better, and you quite literally get to know every single character in one way or another. And if you think The Hunger Games has a better story than Battle Royale, then you are obviously not mature enough to comprehend the latter. In conclusion, if Cato and Kazuo Kiriyama (the boy in the movie who doesn't talk; the one who Kawada said had "signed up willingly for this sh**", though his character is different in the novel) were to get into a battle, Kazuo would win. He's smarter, more resourceful, and has a much better technique in approaching the game. Not to mention the Battle Royale characters actually have substance. Sigh. And yeah, Shogo Kawada smokes almost the entire time that he's on screen, but he's really not the worst role model in the world. He's loyal, driven, highly intelligent, and a pretty good leader. He had the makings of a true freedom fighter, and he's the type that you wouldn't mind letting your daughter go out with (well, after you got to know him).