PS1 should be just fine without sticks since it released with a dpad only controller. Most of the games are either designed exclusively around the dpad or with the option to choose, and off the top of my head there's only two major games that require it - Ape Escape and Alien Resurrection. Some games are definitely a better experience with it, though
I didn't know it could handle Dreamcast though! That definitely needs sticks. I know it can do *some* N64 and that's analog heavy too
Love my Thor, that's the reason I'm selling almost all the rest, lol. Keeping that and a Retroid Pocket Classic