Ok, I'll bite... Why don't you want to install Steam? Just curious.

Consider Chess. LiChess, the site I linked, is free with no ads. You can play on the website or in their mobile app. They will match you against players of comparable skill, so you shouldn't get annihilated too often. Or you can play against the computer to practice.

Super Auto Pets is simple and can be played for free in a browser. It’s a team building game that puts you against other players’ teams, so it’s competitive in that regard.

If you like Pokémon and consider that simple enough, Pokemon Showdown is a free online battle simulator for competitive battles against other players. You can even do “random battles” that just instantly throw you into a match without requiring you to make your own team

Try Gwent. It’s a card game that’s really fun and competitive.

You like card games? I used to play Magic in High School, but I ain't got time for two hour matches anymore.

I've been playing Hearthstone pretty consistently for the past 6-7 years. It's similar to Magic, but much more simple and fast paced.

The more you play, the more cards you unlock and the more competitive of a deck you can play. You CAN spend real money, but I rarely do. I can usually get 50-60 "free" packs by saving up my gold between expansion releases.

There are many similar games out there. This one's my favorite, but feel free to check out some of its relatives! Good luck!

krunker.io is a fast based shooter game with alot of jumping that can be played in the browser.

also have you considered mmorpgs? ill list some that are light? realm of the mad god. runescape/old school runescape. albion online tibia

yeah those are the only lightweight ones i know about that dont take up too much space...

Crawl stone soup is a classic style rogue like you can play in the browser. It has depths (that's a pun you'll see if you get far in it), but a minotaur berserker is pretty straight forward.

There are tournaments every so often where you can compete with the community for high scores and winning different combinations. You can also play offline if you prefer. It's single player aside from this aspect, and meeting computer controlled ghosts of other players.

https://www.brawlhalla.com/

Rocket League. It's fun as long as you don't get sweaty over it.

Board Game Arena! It's free and lots of great turned-based games you can play at your leisure, all through the web. Its wonderful!

Old school RuneScape

King of Dragon Pass i think just got a release on mobile, and if not it's on GOG.com

Age of empires 2: definitive edition Not free but often discounted for a couple of dollars

If you're open to playing games on your phone, I have a couple competitive games that I can reccomend. All these games have micro transactions and battlepasses, as is tradition for monetizing mobile games these days, but they do not provide an edge over opponents, with the exception of possibly Brawl Stars. Most are cosmetic or pay to progress. None of them have any external ads you must watch:

Wild Rift - very action oriented and team based. It can be quite intense at times, so I'm not sure I would call it relaxing for most. But it's fairly competitive.

Legends of Runeterra - From the same company, has the same characters as Wildrift, but is a card game that sits somewhere between hearthstone and Magic in its complexity.

Brawl Stars - very bright, colorful and cartoony. Team based action, with many different game modes. Similar idea and control scheme to Wildrift, but with much simpler objectives. In turn it feels much more casual. Has maybe the most aggressive minimization of the three in terms of it being in your face, but you can still play it for free.

I like playing Tetris. You could either play 1v1 or battle royale style. It’s pretty frustrating at first but when you get a little good it’s basically second nature

Best ones I know are Jstris or Tetr.io. Jstris is more minimal and good if you don’t like flashy graphics and Tetr.io is basically the opposite of that.