As other answers have explained, USB requires bi-directional communication as part of the way that it works. PS/2, while allowing bi-directional communication, doesn't require it in order to send keys to the computer, but does require it to set the keyboard LEDs.
Theoretically, you could build a device to duplicate the PS/2 signal and send it to a second computer, and discard any commands from the computers, so you'd be able to send your keypresses to multiple computers but the keyboard LEDs wouldn't respond to the num lock, caps lock, and scroll lock states (or any other change of LED state, for example in Linux the keyboard LEDs are sometimes used for alternative purposes).
I'm not sure how complex such a project would be. It's been a while since I worked with PS/2, so I don't know if you could simply bridge a couple of wires/connectors or if you would need an active device (e.g. microcontroller) to pass commands in one direction but discard them in the other. If you did have a microcontroller, you could even make the device such that it can interpret the keyboard LED commands and "combine" them for display (e.g. long flash the LED if it is on on computer one but off on computer two, short flash the LED if it is on on computer two but off on computer one, LED steady on if it is on on both computers, and LED off if it is off on both computers). That would be more advanced though.
Also, if your goal is to be able to control one computer from another computer, or two computers from the same desk, or whatever, you might want to look into:
- VNC (allows controlling one computer from another over a network)
- RDP (also allows controlling one computer from another over a network, built into Microsoft Windows but requires the Professional version)
- KVM (a piece of hardware that lets you switch one set of peripherals between two computers)