The presence of the category of gender is connected with the development of the morphological opposition of nominative/accusative. In those systems where the special form of accusative is attested, the category of gender exists.
Standardized
IF there is an accusative case distinct from the nominative, THEN there is a category of gender.
Is this universal about languages or about particular words or word forms? For example: In German, plural NPs never distinguish an acc from a nom, nor is there a gender contrast. Same for feminine and neuter singular. In masc sg, there is a distinct acc, and genders contrast. Thus, the language as such is in line with the universal, and so are all its word forms. But this need not necessarily be the case.
Is this universal about languages or about particular words or word forms? For example: In German, plural NPs never distinguish an acc from a nom, nor is there a gender contrast. Same for feminine and neuter singular. In masc sg, there is a distinct acc, and genders contrast. Thus, the language as such is in line with the universal, and so are all its word forms. But this need not necessarily be the case.