My gut reaction is that I don't agree with you, but I can't immediately put into words why. I think it's possibly that I view a "console" for gaming as a combination of a form factor and development environment and this seems to fit that bill.
I'm interested to hear the other side though.
Otherwise, are stationary PCs custom built for only gaming, such as those used at e-sports tournaments, consoles? They don't have the same customized software stack, but neither does the Deck in comparison to a PS5, imo.
Is the ROG Ally a console? What if I load SteamOS 3.0 on it? Is the PS3 with Linux on it still a console? Are gaming-focused phones consoles? They have vertically integrated hardware and software, and are made with gaming as a focus yet can be used as somewhat general purpose devices, just like the Steam Deck.