I like Levy's gravity-turns-it-into-a-sphere definition.
They should go with that and then just sub-quantify like they do with stars. Ok, we know what a star is, but there are red ones, yellow ones, little ones, big ones, etc.
With planets we have "terrestrial" (or silicate) planets, gas giants, and icy dwarfs. Why do the icy dwarfs have to be out of the picture? Pluto has the land area of Africa and probably Europe combined. It's a planet.
Pluto is probably rocky, probably everything (even comets) are rocky, but have more or less gas either liquified or frozen; Jupiter, Saturn, Uranus, and Neptune are believed to have rocky cores, Earth-sized or better.