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.

[–] Successful_Try543@feddit.org 3 points 3 months ago* (last edited 3 months ago)

Yes, Schweizer Hochdeutsch is standard German without the ß, and some local words uncommon in Austria or Germany. Basically this is what newspapers as the NZZ are written in.
Schwizerdütsch are the Upper German dialects spoken in Switzerland and around, which, if written down at all, like OC said, don't follow a standard orthography.
Thus, you can find Schweizer Hochdeutsch on the chart, but not Swiss German, Schwizerdütsch.