If I was rebooting Q*Bert, I'd probably want to play into the 70s-nostalgia-for-the-50s aesthetic that the Saturday Supercade version used. It's really random as the closest thing to a 50s period concept in a Q*Bert game is Slick's hairstyle and sunglasses, but the world of Q*Bert is kind of random as is, with the only part of the original game that feels particularly intelligently designed from a worldbuilding/aesthetic perspective being that a character who hops on cubes is shaped as a Q. Plus I feel that modern-but-pre-80s eras are very overlooked in gaming.