You're doing for competition what Trump does for... Everything.
Even the example of the second definition is contrary to your very liberal use of the term. You're conflating the trait of being competitive with the noun competition. The second definition also doesn't say anything about informal competition... At all, but it does reference a formal competition.
But more to my point, which you said you were interested in, context is important. Being competitive in martial arts is not the same as training for a competition. Just like training like a cop is not the same as training because you are a cop. Or confusing a fitness bootcamp for actual boot camp because you're going to be deployed to Syria.
If I seem a little frustrated, it's because this is, to me, such an obvious, fundamental truth that I am confounded how you and others fail to understand it. And I hold you to a higher standard because your business is adult learning.