Sorry, but that’s pure pedantry. Way off base.
When one (such as yourself) uses the “public employee" argument about job expectations, the basis behind the argument is that public employees are paid with tax revenue to do a job that impacts and directly affects tax paying citizens. A truly valid argument when the person in question is a teacher, politician, government engineer, prosecutor, judge, etc. Those people are held to a higher standard because their duties directly affect the interests of taxpayers and society. In other words, you and I involuntarily give public employees part of our paychecks every two weeks to provide services that we depend on as a society, and we expect their jobs to be done in our best interest.
Iowa football coaches are not paid with tax money, and they are not performing a service that affects our lives materially in any way. If you get mad at a football team losing, that’s on you. No one is forcing you to spend your money on tickets, tv subscriptions, hoodies, or donations. Because of that, football and other coaches have no duty to you or me to meet any expectations you might put on them.
So no…they are not public employees. You can call them public employees all you want and make whatever semantic arguments you want, but they’re not beholden to you or any other member of the public.