Alvin Kamara suspended for 3 games

Retire means to leave one's job and cease to work. The day he quit, I think he knew he wanted to coach again in the NFL. That's not retiring. He wanted out of New Orleans for whatever reason. It doesn't matter since he's no longer here, but semantic wise, he quit and went looking for another job. He didn't retire.
He did leave his job of being a head coach and ceased to work for a year, so by your own definition he retired.