I always thought "playstation" was a clever bit of marketing on the part of Sony, who from the outset saw the console as something that everyone should play, not just the kids. At work you go to your workstation, whether that's a cashier's register, computer, or factory spot, but when you come home you go to your playstation, and have some fun.
Admittedly in 2020 the "workstation" moniker doesn't really apply to many white collar jobs, but it is sort of perfect if someone thinks about it in these terms. At least it's a better and more meaningful name than XBox