I recently came across the competitive tile-matching game Magical Prisma, it has a Linux version and you can test it out free while it's in Beta. Personally, I quite like tile-matching games when I want to do something a little different and so the idea of a competitive one sounds quite good.
Their rough video below will show you what to expect from it:
For the full game they're planning to have multiplayer for up to four people both local and online, a 140 level campaign, 10 different characters, a competitive league and even tournaments. Some pretty big plans there and it will be interesting to see if they're able to make it. They need a little work on their English text but otherwise, it actually seems like it could be quite fun when everything is in.
As someone who enjoys competitive games with 500+ hours in Dota 2, nearly 400 in Rocket League and a rapidly growing amount in CS:GO thanks to Danger Zone, more fun competitive game ideas will be welcome on Linux.
Find the free beta on itch.io.