The aesthetic is really only accurate to the SNES era of games, which isn't surprising considering it's literally called Super Nintendo World.
They've referred back to that style in some newer games, so it's not solely contained to the SNES, but most of the main Mario titles from N64 on haven't really looked like that (similar in some ways, but quite different in others). I have wondered why they went with that specific era instead of going with something a bit newer, since that era is really targeted at people in their mid-30s and older.
As an aside, the Mario Kart ride looks abysmal. They really messed up there.