As a professional linguist, I think that Farmer et al. are probably right and it's almost surely not a "writing system" at all. (This is a term of art with a very specific sense.)
It's about productivity. If it's purely pictographic or idiographic, it can only encode precisely what the symbols mean. When cuneiform, for instance, went from its early pictographic/ideographic stage to a rhyme, rebus and initial stage, it went from being just a "tagging" system to an actual writing system, where anything that could be said could be encoded.
Would you care to enlighten us?