@theldras times and values have changed. This King is 'violent' because he also needs to teach his son how to NOT DIE on a battlefield. As future king, the prince have that much responsibility.
On a general basis, about 20 years ago, people still cane their children (or students if school) when they misbehave quite often (at least in my country.) Now its apparently considered child abuse and sexual harassment.
Like Walter said as well, this is not considered strict since you technically have your freedom aside from things like throwing a tantrum, staying up late, etc. You can still play games, go out with friends, etc.
A strict family? No games. No TV. The moment you are home, you HAVE to study. You get scolded and punished for scoring less than a 'ridiculous desired value' in exams (usually less than 90 or 100 in more extreme cases). Your birthday presents are all books and study materials. The list goes on. Basically, your life is as controlled as a virtual pet/child in a game like Monster Rancher, Princess Maker, etc. You like running? Want to boost your STR stat? TOO BAD! I WANT INT! MUHAHAHAHA.