We were also the kids who were the most into computers at the time, and eventually the teacher realised that if they were on our side, they could use us to help teach the other kids basic computer skills (office, etc), by using games as the incentive.
If you can't beat them, have them join you...
Edit: We have reached max depth it seems, so I will just update stating that I suppose the change in the scene is quite drastic. Back when I was in school, maybe 5% of the class were computer literate. I felt like a god in that place, being able to help the "smart" students do basic things like creating an email address.
The fact that the teacher doesn't see this as an opportunity is what surprises me. If the work is so boring that kids would rather play games, then use gamification to exploit this behaviour.
In a little Aussie country town, getting computers linked together was a huge boon to our gaming horizons.
Under these premises, teachers in standardized environments are already in an impossible situation.