Being competitive means satisfying all the requirements needed to achieve the outcome desired, however the actual achievement may depend on the level of competitiveness. Competitiveness is one of the measures of eligibility rather than being an inevitable element of success in all situations.
As defined earlier, success is about achievement of the set goals. It could be relating to business, family, job, way of living life, studies etc. There are of course some areas when a person needs to be competitive for having achievement of what he wishes to achieve such as some exams of competitive nature. However, no one is born as competitive. One can develop the required competency with continuous hard work, confidence, perseverance and belief in self. There are even times when competitive people lose out and "luck" factor plays a key role. Hence, "fortune" is one factor which can even cause impediments in the way of competitive people.
Success really depends on what one is searching for in his life. If you are a chain smoker for about 20 years and you are really struggling to remove this habit of smoking and you are able to achieve this, it would be termed as success. One does not need to be competitive for this.