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:
The government is not infringing the victim's freedom. In that sense they have the freedom of speech, de jure.
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?"
This overlaps with the difference between "Positive" and "Negative" rights. Positive rights are those things which society is obliged to provide/create for you - e.g. in the United States you have, when arrested, the positive right to competent counsel (the right to an attorney, if you cannot afford one, the state is obligated to provide you with a public defender). Negative rights are those which the government of a society is obliged to not interfere in, but your fellow citizens are not required to provide it to you.
Your right to free speech is the latter. Your right to be free from violence by your fellow citizens is the former (manifested as police making arrests of people who commit such violence).