Without video games, Twitch would not be what it is now: a live-streaming platform with millions of devoted viewers and broadcasters, some of them with tattoos of the company’s logo. But the company, which Amazon bought five years ago for more than $1 billion, has ambitions beyond serving fans of Fortnite and World of Warcraft.

On Friday, at the annual TwitchCon event in San Diego, the company will show off a refreshed design while unveiling an advertising campaign meant to emphasize that Twitch is an all-purpose live-streaming platform, rather than just a medium for showing video-gaming sessions that can go on for hours.

The campaign arrives after Twitch lost one of its biggest stars, Tyler Blevins, known as Ninja. Mr. Blevins, a gamer with 14 million followers, kept viewers entertained with his running commentary as he worked his way through marathon sessions of Fortnite. In August, he jumped to a rival streaming service, Mixer, which is owned by Microsoft.

Twitch faces intensifying competition from live-streaming services such as Mixer and Caffeine, a social broadcasting platform that received $100 million from 21st Century Fox last year and was part of the Walt Disney Company’s start-up accelerator program.