It's not really, but that is an enlightening comparison. Using the prisoner's dilemma as an analogy for this hiring situation, the employees aren't players (prisoners, if you prefer) at all. Which is exactly the problem.
That just gives you the reason why two companies would want to collude and would have to agree to collude to get the best outcome for both companies.
I agree the more important issue is as you say; the legal and moral aspects are what they are because of the fact that employees are being treated as resources or pawns. But that means that we are happy to see a prisoners dilemma dynamic here, it means that there has to be some type of collusion to make this dynamic happen. Collusion is explicit and detectable. Much better than the various other types of exploitative dynamics that are emergent.
Okay, but the problem itself is different. In a classic prisoner's dilemma the players cannot know how the other will decide and so they act in the manner which benefits them the most. When pursuing their interests they both rat out their accomplice, with the ironic outcome that neither avoids punishment.
> But that means that we are happy to see a prisoners dilemma dynamic here, it means that there has to be some type of collusion to make this dynamic happen. Collusion is explicit and detectable.
Okay, but the collusion is why it's not a classic prisoner's dilemma, I would think.
Also, we're not that happy. The collusion means the companies can avoid punishing one another prisoner's dilemma style. Great for the companies but bad for the employees, since "punishment" in this context involves... hiring.