That's the thing. This definition includes Pluto but it also includes Ceres, the largest asteroid. It also includes Eris (of course since Eris is even larger than Pluto, any definition of a planet that includes Pluto must also include Eris). And it includes at least six to eight Kuiper Belt objects like Quaoar (the scrabble world whose name I've almost certainly misspelled). Plus a couple of scattered disk objects like Sedna which seem to just be out there in weir, random-looking orbits would also have to be included.
And this list would only grow as better telescopes and better survey techniques are developed. Here I think is the real reason that Pluto was demoted. Because it's easier to take it off of the list of planets than to include dozens of small, icy worlds.