Question: What I mean is that is it more dangerous than other contact sports that aren't martial arts? Such as Football, Soccer, Basketball, etc...

And if yes, why?

Answer: 
At a good gym, meaning experienced coaches and decent equipment, boxing/kick-boxing should not be that dangerous. First of all, you're probably not sparring right away, and once you are its in a controlled environment with mouthpieces, headgear, gloves, and shinpads(if kickboxing).

As pointed out in a previous answer, you are probably at an increased risk of facial bruises, bloody noses, etc, but not serious injury. However, if you are training for an MMA style of fighting which includes takedowns, your rate of injury is going to spike sharply.

Comparing it to other sports is tricky. Even at a high-school level we certainly had a higher level of general injuries in football, and typically more severe...broken bones not being uncommon. Basketball didn't have the same high incidence of really violent injuries, but a much higher incidence of high ankle sprains and the like. Soccer seemed relatively safe but I never played at a highly competitive level, and if you watch the Europeans play you'd think it was more dangerous than trying to snuff volcanoes with your bare hands with the frequency they go down screaming in pain.

In short, I think there are too many variables to objectively answer your question, but the above has been my (anecdotal) experience.
The short answer is yes. The very point of the sport is to do damage to your opponent. That being said, the chances of you actually breaking something (apart from your nose) is pretty rare. The only particularly dangerous thing that can happen to you in boxing or kickboxing is a concussion, which can and probably will cause scarring of the brain and make you "punch drunk" after a few years.

So yes, boxing and kickboxing is pretty dangerous, but the types of serious injury is limited to your brain unless you're very unlucky.