Imam Nawawi in his commentary on this hadith states:

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It (i.e. to come to own a slave girl) annuls the marriage between her and her disbeliever husband. ( Commentary on Hadith no. 2643 Muslim)
Thus, we see that in the eyes of Islam this marriage becomes invalid (some opinions like that of the Hanafi school state other conditions required for the annulment to occur).
The critic would definitely argue back stating "what gives your religion the right?" but that is not the point of discussion. This is an external critique of Islam and the basis for this discussion really isn't about this topic in particular but about whether Islam really is true and whether this is God's decree.
To debate the specifics is just useless.
The Muslim sees this decree to be internally consistent and submits to God's law that states that action x results in a divorce.
One might shout out to the Christian as well, "What gives your Bible the right to declare a woman an adulteress if she happened to marry a man who divorced her by not following the proper procedures (Matthew 5:2)?" The Christian really has nothing to say except the fact that he believes that this is God's decree and submits to it. He believes that God has the power and right to determine how divorce should take place (e.g. what conditions are valid for divorce) and submits to them. Well, the Muslim says the same thing in this regard.