The definition of "planet" is a fucked up mess that a small group of astronomers threw together with the intent of classifying Pluto as not-a-planet without really thinking it through.
Like it or not humans have been classifying things from the beginning of our species. Yes sometime we get it wrong or not quite right but we do try and refine our classifications using scientific principles.
Neither does Jupiter. There are about 100,000 trojan asteroids in Jupiter's orbit, so it fails the third criteria; "cleared the neighbourhood around its orbit."
That is just nit picking and is covered by the quote (see below) from your reference anyway. Basically all of that cosmic rubble (call them asteroids or chunks of rock if you will) are orbit crossing and are tiny in respect to the planet which is significantly different. None of the eight planets cross each others orbit however "Pluto" does cross Neptune's orbit which makes Pluto fall under a different criteria than what we classify as "normal planet orbital behaviour". Oh before I forget Pluto's orbital plane is different form the orbital plane of the other planets, read into that what you will.
As per your reference I quote:
In the end stages of planet formation, a planet will have "cleared the neighbourhood" of its own orbital zone (see below), meaning it has become gravitationally dominant, and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence. A large body which meets the other criteria for a planet but has not cleared its neighbourhood is classified as a dwarf planet. This includes Pluto, which shares its orbital neighbourhood with Kuiper belt objects such as the plutinos.
Oh well maybe in the future Pluto will cross Neptune's orbit and Neptune will be waiting for it then the debate will be solved. Of course in a few billion years none of this will matter anyway.