Quest has the documented multiplayer update
Meta published a dedicated I Am Cat multiplayer update for Quest. Use that current Quest documentation and the multiplayer menu in your own build when setting up a session.
Steam VR and PS VR2 are separate answers
Steam labels the game single-player. The PlayStation listing describes offline play rather than promising online multiplayer. A Quest room or video therefore should not be treated as a hidden feature on the other platforms.

Do not assume cross-play
The presence of multiplayer on Quest does not establish cross-play, shared lobbies, or shared progression with Steam VR or PS VR2. Only plan around those features after an official source or the current in-game menu confirms them.
Check after major updates
Read the platform store feature list and current patch notes, then inspect the installed menu. Record the platform and build if the options differ from a recent guide.

Related I Am Cat guides
Sources
Official Meta multiplayer update →

