This is really a question of Language rather than Astronomy. The meaning of words is defined by their use. The IAU has proposed one way of using the word "planet", this group of scientists have proposed another.
Anyone can propose a definition of any word. This group proposes that a "planet" is any astronomical body which 1) Does not have, and never has had sustained nuclear fusion in its core, and 2) Is large enough for gravity to pull it into an ellipsoidal shape.
The intention of this definition is to make a planet defined entirely by "what" a body is, not by "where" it is. Under this definition the classic 8 planets, Ceres, Pluto, Charon, the Moon, the larger moons of Jupiter, Saturn Uranus and Neptune, Eris, Sedna, and the larger Kuiper belt objects would all be "planets" - about 100 known in total. The exoplanets would also be "planets"
Asteroids (except Ceres), comets and other small solar system bodies are too small, and so would not be planets.
The advantage of this definition is that the usually where something is located is not part of the definition of what it is. However, it contradicts several hundred years of use by defining the larger moons as planets.
Unlike the 8 planet definition, this does not have the support of a large international body of astronomers (the IAU). If you wish to use this definition you are free to. I doubt that without the support of the IAU this definition is ever going to be widely used. Most people will either use the 8 planet definition or the 8+Pluto definition.