That's the whole point.
Once his gardening, campfire tending, fish gutting, hammock making, fresh water collecting, palm leaf hat sewing, and wild boar fighting services become automated, he can actually have some leisure and enjoy life...or start working on getting rescued.
You're whole assumption is that what they need to survive is LABOR. That's absurd. What do you think would happen to them if they had robots that create anything their little hearts desire...they're going to DIE from lack of need to labor!? Absurd.
Imagine YOU (yes, you) are literally stranded on some island...are you REALLY saying you would throw away a fish collecting robot (or a FISHING NET, for God sakes) on the grounds it would take away your need to labor?!
(BTW, if you're being facetious, just let me know)