Competition is an instinctive part of humans. No matter what a person may be doing, if another person is doing the same thing, they two will compete against each other, either consciously or unconsciously.
The martial arts are involved with the greatest competition of all, whether you live or die when attacked by another person. When you are attacked by another person, you are in competition with that person and the loser will either be in pain, be injured, be seriously injured, be permanently injured, be gravely injured, or be dead.
Sport competition has been a part of the martial arts since their inceptions. It is a way to test your fighting skills under controlled conditions designed to limit injury so that, when the time comes to defend yourself under real combat conditions, you will be prepared.