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: 
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.
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.