The Dreamcast didn't have a second thumb stick. Even Nintendo added that eventually. I wonder if it would still have the little mini-game in the controller. Memory cartridges went away in the PS3 era, so if they kept it around, it would only be functional as a minigame (and would probably be forgotten about/unused in the cellphone era).
Almost all controllers are the same now, so it would either be aligned sticks like the PS4 or offset like xbox/switch. I suspect the console itself would probably be more similar to the PS5 .. more style and cooling and less square box.