deadpunk
Basically by using a "whitelist" of approved applications and looking for files and executables related to common games.
The teachers would not be responsible anyway, that would be the IT/network admins.
Blocking unauthorised network/internet traffic is relatively trivial by comparison.
The major issue here is that the system is required to be "controlled" not locked down. I am sure that it can be done, but I am not aware of an "off the shelf" product, and feel that it would involve rather more design and development than the school have anticipated. They may well not be prepared to invest in this, and resort to just locking the system down.
This would obviously be unfortunate for the majority as they would be suffering for the stupidity of the minority.
:(