I came to ask for this too, it seems Play Station controllers aren't supported for this game, because I couldn't fully config a Dual Shock 2 connected through 2 different USB adapters which present the gamepad as either a Play Station 3 gamepad or a generic wireless gamepad.
I thought it might be a problem of either the Dual Shock 2 or the adapter, because recent games usually drop support with the Dual Shock 3 generation, but you are having the very same problem I had with a DS 2 so the problem looks like it's from using any Dual Shock controller.
Microsoft really hates Play Station and they go out of their way to prevent people from using Dual Shock controllers, this is the problem, the right analog controller in Dual Shocks isn't properly mapped out of the box to a Xbox controller which is what Microsoft forces you to use inside Windows.
The better, or the lesser evil compatibility for Dual Shock 3-4 inside Windows allegedly comes from using a software called DS4Windows:
https://ds4-windows.com/
and a driver called DsHidMini:
https://github.com/nefarius/DsHidMini/releases in DS4 mode (the software emulates either a Xbox controller or a DS4, mutually exclusive).
I'm in enough shit already to test this and I've got it even more complicated because my setup would be:
Dual Shock 2 -> A dubious Aliexpress grade USB converter -> Dubious driver -> DsHidMini driver -> DS4Windows software
Anyone with a straight DS4 gamepad would have it easier:
DsHidMini driver -> DS4Windows software
So any help is appreciated, the key to make a DS working for this game looks like getting it to be emulated as a Xbox controller with both analog joysticks fully mapped as so.