I just wanted to know if you allow quake II speedruns the ps1 game if they are played on ps2, thanks in advance for any replies

Hi. Sorry for the delay in answering.

Using PS2 console is not forbidden. I know the loading times can be faster for PS1 games when playing them with PS2 console instead of original PS1.

So you can do a speedrun by playing the game with PS2 console :)