FortressOne is a fork of 1996 QuakeWorld Team Fortress. International tournaments are still played and streamed in Twitch. Next weekend there will be players from around the world meeting in Sydney Australia for a in-person LAN event.
SpeedGaming is the place to go for retro game tournaments, both vanilla game speedruns and randomizers. The tournaments themselves are organized by various communities, and SG hosts the live streams. They've got a YouTube channel too, but it usually takes them several months to post the VODs there.
Not exactly an online tournament, but watching German forklift tournaments on YouTube is oddly captivating. I paid for my office chair but I only needed the edge.
My favorite niche tournaments are randomizers of clasic games. I enjoy The Legend of Zelda and Dragon Warrior randomizers the best, but A Link To The Past is probably the most popular I know of.
The Classic Tetris World Championship is also fantastic and it is fascinating how a 40 year old game just transformed in the last 4 years.
If you are into Music, you can give a go to Urban DJ https://urbanpoll.com/dj. It's an ongoing tournament of ordering 5 songs from a specific topic. Disclaimer - I've built it. It'd be fun if more people took part though.