From video gaming to card games and stuff in between, if it's gaming you can probably discuss it here!
Please Note: Gaming memes are permitted to be posted on Meme Mondays, but will otherwise be removed in an effort to allow other discussions to take place.
See also Gaming's sister community Tabletop Gaming.
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This might seem controversial, but you can play chess, either lichess (open source) or chess.com (more popular).
I am not a browser gamer, but i played bonk.io for some time. Its a fun pvp platformer.
Additionally, you can also look for multiplayer indie games on itch. It does not have a lot of multiplayer browser games, but if the laptop is "really trashy", then running games natively should be faster than running them in browser.
It's geo guesser but not enshittified within an inch of its life. They have soooo many fun modes. McDonald's, tourist stuff, really obscure things. Good luck, and don't forget, it's probably fucking Russia anyway
Have you considered retro-gaming? If the laptop isn't much older than 20 years it should probably manage to run dosbox, and with it you can get a ton of old IPX multiplayer titles running, for instance Warcraft: Orcs and Humans, Transport Tycoon, or Command and Conquer: Red Alert.
(Transport Tycoon also has an open source remake, OpenTTD, that can run on a potato. OpenTTD also runs in a browser, but afaik the browser-version is limited to single-player.)
Edit: Of course there is another thing about dosbox: Back then hot-seat or split-screen multiplayer was much more common, so this might also be an option.
I'm not sure if it's still active, but tagpro.gg was my first online multiplayer game that I actually got good at. It's just played with the arrow keys and you controll a little ball playing capture the flag in teams.