SAN FRANCISCO—Toby Ghassemieh is an inquisitive 12-year-old boy with a pet gecko named Coco and the makings of an ant colony in a bedroom cupboard. He built a forge in his backyard with plaster of Paris to melt aluminum into ingots. He wants to be a physicist when he grows up.

All that is on hold, though. What he cares about most is the videogame Fortnite. Same for his buddies Matthew Seiden, Max Howe, Jaren Erville and Reed Leidlein, who all live in or near the city’s Richmond neighborhood.

These...