There is no real way to shut down the sites - unless they are specifically based/hosted in Kuwait. They can try to block them, but then anyone with a proxy bypass or a VPN can get around that stuff. Where there's a will, there's a way....
Here's the Arab Times story today:
Online Prostitution By Arab, Asian Women Widespread
KUWAIT CITY, April 10: The Anti-Cyber Crime Unit at the General Department for Criminal Investigations has announced the closure of about 300 immoral websites, affirming the department will take the necessary legal action against the owners or administrators of these sites.
Sources revealed some people have created websites for online prostitution, indecent activities and night parties. Sources said the websites were shut down after discovery that they promote or encourage indecent practices and sale of illegal or sexual material.
Sources also warned the social media users against wasting time and jeopardizing their future and social life (love this!) by engaging in unlawful and indecent activities. Meanwhile, the daily carried out an extensive investigation on online prostitution websites and smart phone applications, which revealed that this type of prostitution is widespread.
Arab women involved in the act invite interested clients to apartments for KD100 cash or by K-Net. Asian women give their clients the option to purchase KD3 phone card credit, which they will use to interact with their clients to arrange for appointments and payment that ranges from KD20-KD40 (Way cheaper than I had expected...)