What does it mean to be competitive? The dictionary definition simply says inclined or suited to compete. So what does it mean to compete? A working definition would be to strive for an objective such a prize. When a person is competitive, they are more likely to see any situation as a competition and have a need to surpass others. In the given example, one party is trying to dominate the other out of frustration and that is not the same.
Here is my operational experience with being competitive. Competitive people do not blow up when things do not go their way. They work around setbacks. Competitive people are results oriented. They know their stats and have a plan to improve them. The most competitive people I know or have coached, compete against themselves. Things that they can't control, do not detract them from their goal.
So let's go back to the pick up game. If you have never been on a junior high playground, this is scene requires a lot of patience. My nine years of experience can be summed up like this. They argue over every foul and no call even though there is no referee. They pick teams with very little attention to winning the game. They rarely pass the ball. I have to ask them why no one is setting screens before they will do it. The biggest thing that stands out, is the mouthing. It is a hallmark of boys at this age. This is the reason why some do not choose to play, because it becomes too intense.
Here's the bottom line. Competitive kids don't give in to the mouthing. They beat you and shut you up. I loved playing pick up ball in school. The best players were the most quiet players. They didn't need to show a fierce attitude to make up for a lack of ability. My students get frustrated with me when they complain about mouthy players. I always tell them to beat them at the game so they will run out of of things to say. That is not immediate enough as a solution for them today, but as they get older it will make sense. So the next time your kid is mouthy on the playground, make sure you know if they are competitive or something else.