Was it real people reviewing you or just some 20 question quiz? If it was just a quiz, I wouldn't worry about it too much, yes they can give you an indication of where you might fall on a spectrum, but are hardly capable of judging if you are "too" competitive. If it was done by real people, you might put a little more stock in it, but keep your life strategy in mind. If the response is from peers, they probably feel like you are breaking "union rules" for productivity and making them look bad. If this is getting you ahead in the company, rock on. In just a few years you will FIRE and never have to see these people again. Almost all the higher-ups in my company are extremely competitive, it is what got them there in the first place, and they don't care what people think about it. They are smart enough to know not to humiliate others though (most of the time) because it destroys loyalty. If it was from your manager, you might listen a little more closely, as you want to continue your climb up the ladder.
I would not consider myself over-competitive, but I do turn it on from time to time when I can see a clear, tangible, and substantial win. Otherwise, I compete just hard enough to get most of the value, but not necessarily the "win". It's an efficiency thing.
In summary, apply it when it matters, and don't be too much of a jerk!