I cannot believe you are arguing this point. The #2, common usage definition of "professional" is
"engaged in a specified activity as one's main paid occupation rather than as a pastime: "a professional boxer." I added the emphasis. You implicitly concede the player is a subcontractor. Someone else pays the athlete to play a sport for a specific school. That is specifically how, big picture, NIL works.
You are conflating or perhaps confusing "professional" with "employee". True, the players are not W2 employees. However, someone is paying them to play a sport for Iowa as their main occupation, unless guys like Kayden Proctor have some other way to earn a million a year at age 18. It's the receipt of money or other things of pecuniary value for performing a service that makes a "professional".
Your law student analogy also shows you are using a very limited specialized definition. Yes, there is a special legal category of licensed professionals, covering every profession from barbers to undertakers and every other "profession" for which one needs a license from the state. However, even that definition fails you because the definition of a "statutory professional" only applies those to the limited number of occupations that require specific training and public oversight.
So while the players aren't W2 employees, the University has a 3rd party pay them to play sports for the University. The player still gets paid, with money, cars, future contract benefits, etc... for playing sports, which by definition means its no longer a pastime or hobby.