This may end up in the realm of political philosophy rather than politics per se, but you're basically talking about the difference between *de jure* (in the law) and *de facto* (in reality).

There's two things going on here that need to be acknowledged: 

1) The government is not infringing the victim's freedom.  In that sense they have the freedom of speech, *de jure*.

2) An act of violence is being perpetrated by their fellow citizens, from which (we assume, since you do not mention) the state is not shielding/rescuing them.  This means the state has *de facto* ceded its responsibility to the arresting organization.  This means either that organization is *de facto* legitimately acting on behalf of the government, which invalidates #1, above and your answer becomes "No, it does not."  Or the state is impotent to enforce its own laws.

In the latter case, it's less a question of "does the country have free speech?" and more a question of "Does the country meaningfully exist in the first place?"