along with related concepts such as energy and force
EM also studies forces in the end. The intermediates of EM fields are just that--intermediates--to be able to study the forces on charged particles. EM is not only a study of motion, the "fields" themselves are studied, but it falls under this definition by the virtue of it (partially) studying motion. Thermodynamics is more of a study of energy.
If you feel that EM and ThermoD don't fall within the definition, then neither should Gravitation by the same logic. What we'd be left with is mechanics, and then only a half-baked version, as we have no way of generating the forces which we analyse.
Actually that definition is written the way it is because physics' old definition doesn't really work. The classical goal of physics was to be able to predict the positions of bodies after a certain time if their initial positions, as well as the forces acting on them, were known.
If you see the second citation on Wikipedia, Maxwell said something similar:
Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events
With quantum mechanics, this has been proven impossible, so physics is left without a purpose. Redefining physics on the basis of "predicting probabilities of events" seems too focused on quantum mechanics, so the definition on Wikipedia is a sort of diplomatic compromise between classical and modern physics. If you look at the Wikipedia page on Mathematics, the definition is even more abstract. It does span all the fields of Mathematics, but only after thinking about it for a long time (Fields like game theory &c look out of place).
"The study of nature" would be a good definition, except that then biology and chemistry get swallowed by physics. Then again, it's all mathematics.
The bottom line is, you can't really define stuff as abstract and volatile as physics. The best you can do is write a vague definition that can be twisted to encompass all aspects.
Edit: Second question:
The lumping of matter and motion is sort of justified. In the classical sense, it's perfectly fine, as matter causes motion, and matter is affected by motion. If they were kept separate, even in modern physics, we'd have a bit of an issue, as still most motion is matter-related and vice versa; so it's convenient to lump them together. A better way to put it would be a "study of momentum and energy". That's still valid.