who gets to decide?
Usually, lawfully elected lawmakers get to decide. Some Muslim countries allow polygamy and this does not create problems with other countries that do not allow it. But Chechnya is a part of Russia. Russia fought long and hard not to let it break away and create a separate independent state.
Doesn't Russia have a law prohibiting bigamy? If it does than this marriage is unlawful and the man should be incarcerated. If Russia does not have this law then there is no problem.
I am not an expert on Russian law. You tell me, if there is such a law and was the law broken or not.
This is a quote from Wikipedia:
Polygamous marriages are not recognized in the Russian Federation. The Family Code of Russia states that a marriage can only be contracted between a man and a woman, neither of whom is married to someone else.[1] Furthermore, Russia does not recognize polygamous marriages that had been contracted in other countries.