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.
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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!
Rocket League. It's fun as long as you don't get sweaty over it.
Age of empires 2: definitive edition Not free but often discounted for a couple of dollars
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...
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.
King of Dragon Pass i think just got a release on mobile, and if not it's on GOG.com
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
Are random battles with random generated pokemon and random moves and abilities? Sounds fun!
I love pokemon battles but making teams is sometimes a p in the a
Yeah it gives you and your opponent 6 random Pokémon each, but the moves and abilities are pulled from a small list of potential “competitive” move sets for that Pokémon. Then the levels of Pokémon are adjusted so that stronger Pokémon are a slightly lower level to balance things out.
It’s very fun to sit down and be in a battle within 10 seconds, but it can take a little bit of practice to get used to quickly reviewing your available moves for your whole team.
You can even play without even making an account and then you can create the account later if you want to save your progress
Ok, I'll bite... Why don't you want to install Steam? Just curious.
I am not a gamer. very rarely game, and when I do, I use it to distress.
I've seen it on my brothers laptop forcing updates at (almost) every system start-up, taking up more and more space, so I don't want to clutter my PC with more stuff I don't frequently use. or with a software that acts rogue on my pc. (I dislike auto-update) that I disabled them on windows even at a security cost.