That's because back then the Xbox controller was the only controller with good support on Windows. It was designed with the intention of being used with a Windows PC. Back then when you played a game with a different controller, it would still show you Xbox buttons. Even games like Dark Souls which are ported from the PlayStation.

Writing symbols/characters on the button or coloring them doesn't really change the controller in its foundation because you can map the buttons in any way you like anyway. What separates gamepads from each other is the layout and amount and type of buttons you have. The type here is an input-type meaning analog/digital, trackpad whatever. I also wouldn't call the Steam Controller a Xbox or PlayStation controller, it's a unique gamepad ... a Steam Controller.