If we talk about 'syntax' as part of grammar (ie ‘sentence structure - subject, verb, ‘predicate’) , then stories, newspaper articles, poems, plays, songs, films all have their syntaxes too.
What is the grammar/syntax of a paragraph? What is the grammar/syntax of a page? Of a chapter? Of a picture book? Of a short story? Of a novel? Of different genres of writing? If we want school students in primary schools to write, why is it mostly the grammar of the sentence in the National Curriculum?
What is the grammar/syntax of song? Of poems? The TV shows that the children watch? How does the grammar of conversation work? Or of drama?
Or: is this a fable? A parable? An allegory? Or: is this a folk tale? (Vladimir Propp wrote a book which is essentially the 'grammar' or syntax of folk tale. He called it 'morphology' but that's part of 'grammar'. )
Another way to think of the 'grammar' or 'syntax' of different kinds of writing, is to think of these as 'agendas'. An agenda for a meeting is a kind of grammar of the meeting.
What are the agendas for different kinds of writing and speaking?