It's "inevitable" that competitive video gaming, also known as esports, will someday be part of the Olympics, Logitech International President and CEO Bracken Darrell told CNBC on Tuesday.

Darrell, whose company makes computer and mobile phone accessories and has begun to sponsor top esports teams, told "Mad Money" host that Logitech met with the International Olympic Committee two weeks ago.

Held in Lausanne, Switzerland, where Logitech is headquartered, the meeting revolved around "how and when" esports should come to the Olympics, Darrell said.

"I think it's inevitable. I think it will be part of the Olympics," Darrell said on Tuesday.

"I'll make another prediction which it'll be hard to hold me to unless you have me on the show in 10 years or 20 years, but I think it'll be the biggest sport in the world," the CEO added.

Competitive gaming has swept the country as high schools and universities warm up to the idea of creating programs and scholarships for students who excel at games like Activision Blizzard's Overwatch and Riot Games' League of Legends.

University of California, Irvine, whose acting esports program director Mark Deppe appeared on "Mad Money" in January, was one of the first universities to offer esports scholarships, awarding gamers $5,610 and $2,500 to join its League of Legends and Overwatch teams, respectively.

Logitech is a partial sponsor for UCI's program, providing high-end gear for the school's esports facility.

"Scholarships are starting to spread across the university system," Darrell told Cramer. "My brother's a college president, Kentucky Wesleyan College. It's a small liberal arts college. They're putting in gaming as not a varsity sport yet, but a club sport. It's coming everywhere."

And that trend drives sales at Logitech, which in late July reported first-quarter earnings with more than 60 percent growth in its Gaming and Video Collaboration categories.

Darrell added that video gaming has reignited growth in his company's webcam business, which is seeing double-digit gains as gamers and bloggers seek higher quality video equipment to film themselves playing games.

"In 1965, 1968, 1969, I remember the NFL and the Super Bowl, how big it seemed then. Looking back on that, it was tiny," the CEO said. "I think that's exactly where we are now in gaming."

Shares of Logitech closed up slightly on Tuesday, logging a 0.13 percent gain and settling at $45.79 a share. In its July earnings report, the company said it would acquire microphone maker Blue Microphones for $117 million in cash.