It is a premise of the philosopher’s argument, not Graham’s. It directly contradicts Graham’s premise.

This is the function of the referenced claim. If people can be truly happy while doing nothing at all, then Graham’s premise (people must do something in order to be truly happy) is false.

It’s the philosopher’s premise—the philosopher doesn’t reject it. It is also not an analogy; it’s a direct example of an activity that runs counter to Graham’s premise.

The philosopher never outrightly rejects Graham’s conclusion. She doesn’t say that the best life is not a life full of activity—she doesn’t take a position on what the best life entails. Her conclusion is only that Graham’s argument is insufficient persuasion.

It is a premise for the philosopher’s main conclusion. The fact that people can be truly happy while not doing anything disproves Graham’s only premise, which in turn supports the conclusion that we shouldn’t be persuaded by Graham’s argument.