The linked question explains why writing isn't language, but the embolded sentence is alleging something different, that writing isn't even "part of language". Why?
Linguistics usually divides language into various levels. In Figure A.1, meaning, sound, and writing are considered part of the outside world, not part of language. Language is the cognitive structure linking meaning and sound. We can see from this figure that semantics is the part of language most closely related to meaning, and that phonetics is the part of language most closely related to sound. Writing has a more complicated relationship to language in that units of writing are commonly related to both morphology and phonology, but not generally to semantics, syntax, or phonetics. To illustrate the different levels, we will analyse the sentence Mary purchased a new bookcase; this analysis will be followed by other examples for each level.
Henry Rogers, Writing Systems (2004), p 281.