Most "2 player" lists online are one-player games with a leaderboard. These are not. Three of the four below are played by two people on the same keyboard at the same time, which is the thing that actually works in a classroom, on a sofa, or on one laptop between two people.
Kung Fu Arena is the one built for it: a best-of-three fight where player one moves on WASD and punches with F and G, and player two moves on the arrow keys. No split screen, no second device, no code to share - you both just put your hands on the keyboard.
Chess 3D and Ludo Legends are the pass-and-play pair. The board is on screen, you take turns, and the device goes back and forth the way it would across a table. Ludo takes up to four. Both also play against the computer if the other person leaves.
Transform Race is the odd one out and worth knowing about: it is online rather than same-device, so you open a room and race up to three real people wherever they are.
All four are free, need no account, and start the moment the page loads.
