Comment by Xirdus

Cool, didn't know that. I thought they've got rid of pressure sensitive buttons in PS3 already, not PS4. Thanks!

So apparently, to make pressure sensitive PS2 controller work in PCSX2, you need ShanWan PS2-to-PS3 adapter (or equivalent), DSHidMini, and set input mode to SDL. Since I lack both pieces of hardware, I can't test it myself. Or skip the middleman and get a PS3 controller, which is a better option anyway for several reasons.