Microsoft Corp. on Thursday is launching its own videogame live-streaming service called Mixer, setting up yet another battle among some of the biggest names in the technology industry.

Despite its long history in videogames, Microsoft is late to live-streaming, in which people watch real-time videos of other people playing games and esports contests. It faces competition from the leaders, Amazon.com Inc.’s Twitch and Alphabet Inc.’s YouTube. And Facebook Inc., which has two billion monthly users, this year signed esports...