> So the key distinguishing attribute that makes a "game console" a "game console" is its walled-garden nature? Nothing else?
Practically? Yes, IMO. You can say it uses specialized hardware manufactured on a massive scale, with each gen being a distinct set of hardware with slight variations, but then you're describing an Apple M1 Macbook Air or Microsoft Surface.
People have and will always gain root access, but the OEM doesn't typically like this, and goes out of their way to prevent it. There may be APIs the OEM leaves open to allow the creation of, for example, XMBC, but an XBox is hardly an open, general-purpose, computing platform.
If you want to call it a console that can play games, then my custom-build Linux computer console fits that definition. Hell, I wouldn't have to even leave the computer console TUI to play Dwarf Fortress.