In short, yes, but with some caveats. The simple answer is based on an assumption that the bulk composition of hypothetical other planets are not that different from the rocky planets of our solar system and more broadly that the bulk composition of our solar system (which sets the available elements for all of the planets in that solar system) are not that different. If we accept that assumption, from there the rocks we observe on said planet(s) would be dictated by the underlying laws of chemistry and thermodynamics (which we would expect to function similarly regardless of location, i.e., reactions between particular elements/compounds at particular temperatures and pressures will still behave the same). In terms of tests of this assumption, we have limited data, but broadly the rocks we've been able to observe (in here I'm lumping a lot of different types of observations) on extraterrestrial bodies (primarily the Moon, Mars) and meteorites conform to and/or are similar to rocks we observe on Earth.

One thing to note though, generally, Earth has a pretty wide array of rocks compared to most other bodies we've been able to explore to some degree. This is primarily due to the existence of active and long-lived mobile lid tectonics, which is the root cause of, or at least allows for, many of the igneous differentiation processes that allow for the formation of intermediate and felsic rocks (e.g., this igneous rock classification diagram) like granite (felsic). In contrast, most of what we've found on planets that either did not have plate tectonics (or had likely short lived tectonics or something like mobile lid tectonics) are ultramafic and mafic rocks and things derived from them (e.g., sedimentary rocks, which are still very enriched in iron and magnesium and thus geochemically would "look" like ultramafic or mafic rocks).

Finally, if we circle back to our original assumption, a lot hinges on this idea that the bulk composition of our hypothetical planet(s), and by extension the solar system and star within which the hypothetical planet(s) formed is similar to both Earth and our solar system/star. The limitations of this assumption are understood and discussed by people studying expolanets, e.g., Putrika et al., 2021 discuss this directly in considering some possible differences in bulk composition (e.g., things like the relative abundance of iron, magnesium, and silicon within a given solar system) and how this might influence the composition of rocks that can and do develop. As a specific example, Putrika & Xu, 2021 highlight that you could expect some exotic compositions in extreme environments (e.g., exoplanets that develop around a "polluted white dwarf").