Early in the Prolegomena, Kant says that both pure mathematics and pure physics are examples of a priori cognition. What exactly did he mean by "pure physics"?
The clue is in the fact that he called it a priori. Pure physics is physics that can be done a priori without relying on experimentation. Here is an example from one of Kant's other works.
All matter is subject to both attracting and repelling forces. If there were no attracting forces between the particles of an object, the object could not hold together. Any disturbance would send the particle all flying off independently. If there were no repelling forces, then the attracting forces would cause all of the particles to converge to a point. Therefore, order for a solid object to exist, the particles of the object must both attract and repel each other.
Note that there is no experimentation here, it's all a priori reasoning.
You're sure to get a better response from Klocking than this, but one should preface any response by saying that Kant's views are open to interpretation. According to the SEP article on Transcendental Idealism:
In the Critique of Pure Reason Kant argues that space and time are merely formal features of how we perceive objects, not things in themselves that exist independently of us, or properties or relations among them. Objects in space and time are said to be “appearances”, and he argues that we know nothing of substance about the things in themselves of which they are appearances. Kant calls this doctrine (or set of doctrines) “transcendental idealism”, and ever since the publication of the first edition of the Critique of Pure Reason in 1781, Kant’s readers have wondered, and debated, what exactly transcendental idealism is, and have developed quite different interpretations. (my emphasis)
It appears you are quoting:
One need only attend to the various propositions that appear at the beginning of proper (empirical) physics, such as those of the permanence of the same quantity of matter, of inertia, of the equality of action and reaction, and so on, in order to be soon convinced that they constitute a pure (or rational) physics, which well deserves, as a science of its own, to be isolated and established in its entire extent, be it narrow or wide. (my emphasis)
According the SEP article on Kant and Hume:
[Kant believed] empirical laws owe their status as “necessary and universally valid” to their relationship with the a priori “pure or universal” laws (principles) of the understanding. (my emphasis)
According to this article on Kant and Science, one interpretation of Kant's views on the sciences, and in particular physics is:
At the top of the hierarchy is physics, which is both proper and rational. Physics, McNulty explains, is rational for Kant because it has laws, and proper because these laws are necessary and can be derived independently of experience. Kant holds that the laws of motion, for example, are derivable from the essential, conceptual nature of matter. We do not, then, infer through observation that matter is subject to Newton’s laws of motion so much as come to realize that matter must be subject to such laws in order to be observed at all. (my emphasis)
Thus, pure physics is the physics that serves as a metaphysical basis for empirical observation. According to WP's article on Kant's use of the term a priori:
Space, time and causality are considered pure a priori intuitions. Kant reasoned that the pure a priori intuitions are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that it has were these a priori forms not in some way constitutive of him as a human subject. (my emphasis)
Thus, the intuitions of physics, the 'pure physics', particularly the physics of Newton which are known through logic and mathematics, come prior to empirical experience as Hume advocated, and we come to know the universal laws of physics through the a priori (as reformulated by Kant) intuitions about physics that are perceived by the mind.