I would argue that a PC without a keyboard, dedicated to gaming is a console.
Was the PS3 fat a PC? It ran Linux.
i’d differentiate it by the kind of it’s ui. linux will still feel like a desktop operating system, made for mouse and keyboard, whereas the console has a controller friendly interface. probably not much of an issue if you boot into steam directly through.
genuinely curious, is there any linux DE that is optimised for being connected to a tv and controlled by remote/gamepad from the couch?