I completely agree with this.
The term "video game console" is used to distinguish a machine designed for consumers to buy and use solely for playing video games from a personal computer, which has many other functions, or arcade machines, which are designed for businesses that buy them and then charge others to play.
So the term, "console exclusive" is warranted, because while it is true that games can be played on a PC, the personal computer has many other functions for use, and isn't designed for the sole purpose of playing a video game as a console would be. So when a game is made for a console, and a PC, it's only fair to refer to it as a "console exclusive" to differentiate it from other consoles, but not from the PC.
As for my personal question...
How would we go about reffering to a game such as, "Dead Rising"...seeing that a game under the same franchise was released on the Wii titled, "Dead Rising: Chop Till You Drop", but offered completely different gameplay experiences, and wasn't under the same storyline as the original for the Xbox 360? Does that justify "Dead Rising" as a Xbox 360 exclusive, and "Dead Rising: Chop Till You Drop" as a Wii exclusive? The Wii version seems to fit your definition of a "remake"/different game under the same franchise label. There was a big issue on this, so it'd be nice for a clarification Naznatips, thank you.