That depends on your definition of “language”, where some definitions are much more scientifically useful than others. Defining language as “a system of communication” is not very useful, since there are important defining characteristics most people, and especially most linguists, believe that language possesses that other more general forms of communication do not.
Under the definition used by most linguists (for the kind of object we’re talking about here, that is - there are many other relevant objects of study that can be called a “language”), spoken/signed human languages have all of the characteristics of language, while “body language”/animal “languages” do not.
Sign language is language, since it has a systematic, unconscious mental grammar that meets all of the characteristics above, and writing is not considered language, since it’s just a means of encoding/preserving a language that already exists.
Another way of stating this is that writing is not itself the output of a mental grammar - it’s the output of a translation algorithm that acts on the output of a grammar, and so can’t be considered language itself (again, under one of the most common definitions of “language” used in the scientific study of human language).