Praise be to Allah.
I do not think there is anything wrong with this, if the women are on their own and the men are on their own, without any mixing in the place where the competition is being held. Rather the women should be on their own, and they should be covered and screened away from the men.
As for the man who listens, if he listens in order to learn and reflect on the words of Allah, there is nothing wrong with it. But if he finds pleasure in listening to their voices, then it is not permissible. But if the purpose is to listen and benefit, and find pleasure in listening to the Qur’an and benefitting from the Qur’an, then there is nothing wrong with that, in sha Allah. End quote.
Fatawa Nur ‘ala ad-Darb by Shaykh ‘Abd al-‘Aziz ibn Baz (2/100).