your original request was just to sort alphabetically:
so if you’re really wanting taxonomic ordering, you may want to change your original feature request.
if you’re wanting to just sort alphabetically by name, i don’t think it would be a lot of steps to copy the results from the thing i referenced earlier, put those into a spreadsheet, and sort by taxon name.
UPDATE: there’s also https://kildor.name/inat/species, which can give you the data in CSV format. so you could just take the CSV and sort as you like. this and other tools made by @kildor are described here: https://forum.inaturalist.org/t/several-external-tools-for-inat-data-by-kildor/19906.