AUSTIN—Ashley Bowling saved up for months to buy a $575 VIP pass to RTX, an annual three-day gaming convention hosted by digital entertainment company Rooster Teeth that attracts young, web-savvy consumers.

But by the time ticket sales opened to the general public, all the VIP passes had been snapped up. The 18-year-old recent high-school grad and her mother, Kimberly, 47, who is also a fan, ended up buying regular weekend passes instead, at around $100 each. Clad in costumes based on Rooster Teeth characters, they flew to...