The PS1 is more than dual-analogue first person shooters though. In fact, those came very late and are mostly present on the following generation. PS1 and Saturn were all about finding out what worked and what didn’t in 3D, like how to make a platformer with a third dimension of movement. Without an analogue stick, even less two of them. If you played your Doom-likes with the keyboard only, you will get an excellent equivalent with a digital controller, with the bonus of having strafe left and right as dedicated trigger buttons. That doesn’t work as well with Quake-likes of course.
On that note, I got to try Jumping Flash 2 thanks to that PS1 Classic trailer. The controls are fairly ingenuous here, for a game in the first-person view without a dedicated view stick, as it’s more focused on jumping onto stuff than shooting at things. Basically the dpad moves forwards/back and turns around while on the ground, and left/right swap to strafe while in the air, for total air control. The camera also automatically aims down if you jump high enough, to help with the landing. You can aim up and down by holding a trigger and using the dpad, but at least in the first level I never had to bother.