Yes, playing ball is labor. It's a job, and the NFL and the teams employ the players for the purpose of making their business profitable. Under the law that's no different than a law firm hiring an attorney or a manufacturer hiring an engineer.
Yes, Zeke being out hurts the team, and I understand your point that the team can't control everything a player does, and therefore it doesn't seem fair to punish the team. But the reality is the NFL is not the only employer that can be negatively impacted by the bad behavior of an employee. If an employee calls in sick too often because he stayed up partying, or he does something that casts the business in a bad light and the business loses sales or clients, or if he gets fired for his conduct and is no longer available to perform his job for the benefit of the company, that hurts the employer.
I suspect the viewpoint of the NFL is that when there are consequences for the team as well as the player, the team is incentivized to educate and police players themselves, and hopefully head off some issues before they occur.
Then, there is the fact that this would never be accepted by the NFLPA in the collective bargaining process.