Just to be clear, it absolutely does establish such rights in law and thereby grant them as legal rights. It may be that some of authors and ratifiers (and some current constituents) of the Constitution have a (quasi- or literally) religious belief about the metaphysical preexistence of and/or independent ethical universal necessity of exactly such rights (or a super- or subset of them) against any legitimate government, but that's...largely immaterial except in terms of arguments between people sharing such views as to what rights should be established in law, or social science analysis of why the particular rights chosen were established in the Constitution.