Well, as a generalization.... all parties control the means of production to a degree. In this instance, there is no ability to command performance as there are no contracts.
Eventually, the players will figure out they have more power as a group whether its an official union or not.
Folks try too hard to generalize concepts, especially when talking about political and socio-economic philosophies.
"Controlling the means of production" is simply this: if you work as a blacksmith, the means of production are a hammer, and an anvil. And maybe a ventilated shop in which they are used. The guy who owns the anvil, the shop, and the hammers, he has a lot of power. The power to hire and fire workers to use his gear, for instance. The power to set prices for the products. And so on.
Now, those workers, they have the power to control their own labor. But that's it. They do not, in any way, control the means of production.
That's what Karl Marx was all in a tizzy about. He thought that was unfair. He thought the workers ought to be given control over not only their labor, but the means of production as well.
The modern college football equivalent would be players arguing that they ought to be part owners of the stadiums, locker rooms, and (very importantly) ticket offices. That they ought to share in ownership of the means of production.
Of course, that's utter horse hooey. The #1 way to destroy an economy is to penalize the folks who have the means of getting businesses going. Every time it has been tried at large scale in history, public (worker) ownership of the means of production has utterly failed.
At the local level, it tends to work okay, in a healthy mix with capitalism. Farmer Co-Ops and church societies, for instance.
My, we've gotten off-topic.
Go Vols!