The language is a variety of German. But there are no real writing rules. Text you see written in Switzerland, e.g. on signage, is practically Hochdeutsch with the needed substitutions of words, like chicken for for example where they don't use the German word.

Written language between people however has no rules and people write as they speak and that's definitely not Hochdeutsch.

Edit: I just read your post again and maybe that's what you meant and I misunderstood you.

Ah damn, you're probably right. Schriftdeutsch.

Orthography. I thought it was a subset of grammar, but no.