I installed pcsx-df 1.10, since that was what was available to me, didn't seem to have an issue setting the controller. I don't have any games handy to test it with, but I don't see why they wouldn't work since the setup went fine.
Screenshot of the controller configuration window:
I think this controller has every button exactly like a PS1 controller, even the buttons under the analog sticks.
BTW: Not sure if Slackware will be any different, but on my ArchLinux system, I didn't have to set up anything at all, I just plugged it in and started playing.