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.
While black eyes and minor bruises or the occasional broke nose are quite common in boxing, i think the devastating injuries like cruciate-ruptures are rare.

From my non-representative experience i'd say that runners, soccer-players and the like usually spend more time with doctors because of knee-injuries or broken ankles than (thai) boxers.

Boxing happens in a very controlled environment, there is only one opponent to pay attention to and the attacks and defenses are well-established. While there is a big strategic component, there is not much creativity going into making up moves on the fly.

Soccer for example seems much less predictable to me. While running at full speed an focusing on the ball one may have to deal with being tackled at any moment.