In his letter, I would assume he's referring to a problems in astronomy and mechanics. But the term physics was much more broad up until the 19th century. This is covered in good detail in e.g. J. L. Heilbron's Elements of Early Modern Physics (1982), chapter $1$, $\S 1$, "The Scope of 'Physics'". Some relevant lines:
At the beginning of the seventeenth century 'physics' signified a qualitative, bookish science of natural bodies in general. It was at once wider and narrower than the subject that now has its name: wider in its coverage, which included organic and psychological as well as inorganic phenomena; and narrower in its methods, which recommended neither mathematics nor experiment. The width of coverage and the depreciation of mathematics derived from Aristotle; the indifference to experiment, as opposed to everyday experience, from the authors of peripatetic textbooks.
'Physics' continued to be understood in its Aristotelian extent throughout the seventeenth century. Molière's bourgeois gentilhomme [(1667)] asks his philosophical tutor what physics is and receives in reply, '[the science] that explains the principles of natural things, and the properties of bodies; that discourses about the nature of the elements, metals, minerals, stones, plants and animals; and [that] teaches us the cause of all the meteors.' Molière's friend, the Cartesian physicist Jacques Rohault, says the same ('the science that teaches us the reasons and causes of all the effects that Nature produces') and he tries to give an account of everything, including human psychology, in a physics text that had a peculiarly long life [Rohault, Traité (1692)]
The transition to the modern meaning came much later; there's not a clear cutoff, but the transition was still slow by the late 1700s. For example, Heilbron cites the Journal de physique (founded 1773), which emphasized natural history, and various sources up to the year 1800 which considered physics to include agriculture and biology.
To summarize: Leibniz' concept of physics (Lat. physica) was a general term including what we would today call astronomy, biology, natural history and psychology. It's safe to assume he's referring in his letter to the more exact of these, which admit mathematical models.