IAAL but I don’t know the answer to this question. The June 30, 2006 edition of The Sporting News magazine (print edition only, apparently) has a big article about how to become a licensed NBA sports agent. Having a license to practice law, or to be a CPA, or a certified financial planner, isn’t a requirement, which leads me to the question: Why isn’t being a sports agent without a professional law license practicing law without a license?
My hunch is that it is practicing law without a license, but that is just my hunch. Does anybody have a good answer?
So your hunch is that every sports agent is practicing law without a license and nobody has ever noticed or said anything about it? Not even lawyers?
Remind me not to listen to your hunches when you go betting. 
You do not have to be a lawyer to negotiate a contract. Business people do this all the time. Agents of every stripe - literary agents, film agents, art agents - do this all the time. You and I can negotiate a binding contract.
We might run into trouble later when clauses are questioned if we don’t get the contract right because of our non-lawyer ignorance, but that’s a different issue.
As I understand it, practicing law means advising someone of their legal rights and/or obligations under the law. I’m not sure negotiating a sports contract involves providing legal advice. The deal is you play ball for X Jillion dollars, + y incentives, + z signing bonus. Now after the deal is made, I can see where questions of interpeting the contract could cross the line into law practice…