Sitting around playing video games is a classic example, but it's a way to become a better video game developer or a world-class player, both of which are fulfilling and well-paying endeavors. Even sitting and doing nothing (i.e. meditating) can be one of the most productive things an individual can do. [0]
What constitutes a "productive activity" is quite subjective. And even seemingly unproductive things can be productive: if they help de-stress and refocus, they're still contributing to productivity.
If I'm playing minecraft and optimize a factory in an hour, that is a productive hour of gaming. But to my father, that entire time was wasted because he cares naught for video games and would instead be out working his farm. But I look at the small scale farm and realize that for what it produces, it would be cheaper to just buy the produce and thus don't see it as productive.
Is watching football and prime time TV productive? What if you have someone who doesn't like either but is doing so only so they can be a better culture fit at work since that is what everyone else at work is doing?