Except anarchists, I think "Randians" and most "free market advocates" are in favor of court (government) enforcement of contracts.
> He was 16
There's a concept of "age of consent" or "capacity" to contract.
> arranging a fake passport stating he was 20
Fraud.
> wages retained
Who would sign a contract like this? It's most likely a violation.
> deprived of the ID cards they need to move around freely without fear of arrest
Seems like a failure of the State, to be arresting people who are allowed to be there.
> demand their wages, a drastic step given that the authorities can simply expel them to penury
If "the authorities" refers to the State, I'd say it's another failure of government, not the free market.
> refusing to issue the exit permits they needed to return home
Yet another failure of the State, if I'm reading that correctly as a restriction of the freedom of movement: a basic human right which brutal, anti-capitalist regimes are infamous for violating (e.g. Berlin Wall). Historically, people tend to flee from less free (market) countries to more free (market) countries.
> the kafala system binds the worker to a single employer
Is "kafala" a system of laws? This sounds like Directive 10-289 which Ayn Rand rails against in Atlas Shrugged: "All workers, wage earners, and employees of any kind whatsoever shall henceforth be attached to their jobs and shall not leave nor be dismissed nor change employment"
One of the biggest drawbacks to the libertarian 'fight-it-out-in-court' mindset is that it considers everyone to be equal, but only if they can afford a lawyer. The people that libertarianism fails the most are the people we're talking about right now.
However you do raise a good point, in this situation the workers are not free to pick up and leave, which invalidates it as an argument against free market advocation. I concede the discussion to you good sir.
(With the exception of the gender assumption, which I'll overlook)
You ruined the spirit of your reply.