Yes, students are not allowed to use inside schools, and it's a good thing. Otherwise, many kids here will be playing pubg mobile, watch video content, or surf in social networks like hell. Many grown up youths here are so obsessed in pubg mobile that they don't notice what's happening in their surroundings, even if they're outside home. Some states in India are calling for bans. This is the scenario in India.
Regarding browsing in school computers, it'd be difficult for teachers or concerned staffs to monitor internet usage of students and control directly. That's why they'll have websites blocked. Sad that you can't help it if a CS GO news website is blocked.