I'm no expert but there's a small chance they didn't setup a WiFi network to facilitate gaming. I'm probably wrong though so you should just ask them to remove the block.
Seriously though, if you want to play connected games during breaks you could always tether your laptop to mobile data. You seem to be asking for help breaking your school's rules and degrading WiFi quality for people using it to do schoolwork. That's really not cool. But if you're willing to pay for tethering I don't think the school could argue with someone playing games on a service they paid for during their free time.
A bus station is where a bus stops. A train station is where a train stops. On my desk, I have a work station…