It’s not a real console because it involves emulation. Much in the same way that the NES, SNES, N64 & GC emulators in the Wii were together called the “virtual console” and not grouped together with the Wii in name.
If I make RetroArch start fullscreen on boot on my PC, can I call that a game console? No, it’s a PC with an emulator. Your scenario is no different, other than it being a Raspberry Pi.
But it’s the whole point of a console to have one targeted platform instead of many.
I did not say target platform. I was talking about individual subsystems. If you cater to all of them, you will end up with a PC-incompatible PC clone. So, since you cannot cater to all of them, you cannot expect more than a very minute amount of developers to target your console as a whole. Hence, you cannot call it “the Itch.io console”.