I don't agree with this. The whole concept of a "console" is that it is a dedicated, closed device intended to do a very fixed range of functions. There is no user-serviceable parts in it and the user is never intended to open and service it. A "PC" is a computer meant to run all sorts of software and it is user serviceable. Basically, "console" implies a specific intended purpose more than what it physically is built from. It just happens to contain similar components than a general purpose PC.
Consoles are really really just general purpose computers.
No it's not. It has a very specific purpose. Which is the opposite of general purpose. No-one argues it can't be hacked to perform some other purpose, but this doesn't make it a general purpose computer because the masses that make it successful are not using it that way.
By your logic a bulldozer is a car because it has an engine, steering wheel and four heels. Yet no-one calls it a car because it was never meant to perform the same duties as an actual car. Yes you can probably use it to go and buy groceries if you really want to. Hey you can probably even hack it and put lowriders on it if that sort of thing blows up your dress...
Or taken even further... The digital clock on my wall is also a general purpose computer because it has a CPU and a display.