Pluto is definitely a Kuiper belt object. The question is just whether it’s possible for the categories “Kuiper belt object” and “planet” to overlap.
You also have to be careful about the “directly orbits a star” part of the definition. Everyone agrees that, say, Titan is not a planet. But what about our own Luna? Everyone knows that Luna orbits the Earth, not the Sun, but “everyone knows” is a notoriously unreliable source of information: In fact, the Sun exerts a larger gravitational force on Luna than does the Earth (a situation unique to Luna, among all the “moons” in the Solar System).
Depending on exactly how “planet” is defined, I can argue for any number from 8 to 18 “planets” in the Solar System (ironically, in one case, shrinking the definition of “planet” actually increases the total number). The longest list I can come up with is Mercury, Venus, Earth, Luna, Mars, Ceres, Vesta, Io, Europa, Ganymede, Callisto, Saturn, Uranus, Neptune, Pluto, Xena, Quaoar, Sedna: This list comes from the definition that a planet is an object large enough to form into a sphere gravitationally (with enough leeway on “sphere” to include Vesta), but small enough that dR/dm > 0 and hydrogen does not fuse in its core, on which the strongest gravitational force is exerted by a star.
Really, though, I think the real problem with classifying Pluto is that we’ve taken at least two completely different types of objects, or three if we include Pluto, Xena, and the like, and lumped them into a single category. I’d much prefer if we had completely separate names for terrestrial bodies like Earth and Mercury, gas giants like Neptune and Saturn, and icy bodies like Pluto and Sedna. This would still include ambiguous cases like Luna (with its peculiar orbit), Ceres (perhaps below the lower size bound), and Jupiter (arguably a brown dwarf), but it would at least avoid the question of whether Pluto is a “planet”.