RavenSky
The Doctor's Wife
The only case where I see mandatory "work" valid is with children: children are in the age of best brain plasticity, and tend to live in the present without believing much in plans for the future, so it's the parents or society duty to keep their future options open by making them work at their education.
Ironically, even children, when left to explore on their own in terms of education, will "work". They will tend to follow the same pattern as your gamer example. One child may be totally obsessed with dinosaurs, showing no interest in sciences or reading or history. But the obsession with dinosaurs will lead the child to reading and science and history in order learn more about those dinosaurs. This is the Sudbury School model, and it is a successful one.
I do think schooling should be mandatory (& free), but more as a means to provide the resources to allow children to learn than any belief that children have to be made to learn. And that parallels my belief that freeing adults from having to work for pay will allow adults to work for self-actualization.