Leaving marks on trees and such is not writing. It is not the transcription of spoken language. We have examples of this kind of symbol-placement on ancient cave art stretching far back into the ice age. It is not considered writing.
Written language is rarely just a transcription. It usually has a number of distinct differences in both lexicon and syntax. There are languages that are only written.
Art is not writing, true. Distinct symbols and syntax are required for writing. But it need not be transcription of anything spoken.